%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ANA003-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 16:32:21 EDT 2024

% Result   : Unsatisfiable 8.92s 9.12s
% Output   : Proof 8.92s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : ANA003-1 : TPTP v8.2.0. Released v1.0.0.
% 0.08/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue May 28 04:31:24 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.20/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.51  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 8.92/9.12  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.VZlQZZUoYY/cvc5---1.0.5_13554.smt2
% 8.92/9.12  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.VZlQZZUoYY/cvc5---1.0.5_13554.smt2
% 8.92/9.13  (assume a0 (forall ((X $$unsorted)) (= (tptp.add X tptp.n0) X)))
% 8.92/9.13  (assume a1 (forall ((X $$unsorted)) (= (tptp.add tptp.n0 X) X)))
% 8.92/9.13  (assume a2 (forall ((X $$unsorted)) (not (tptp.less_than X X))))
% 8.92/9.13  (assume a3 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))))
% 8.92/9.13  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y)))))
% 8.92/9.13  (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X))))
% 8.92/9.13  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y))))
% 8.92/9.13  (assume a7 (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa))))
% 8.92/9.13  (assume a8 (forall ((X $$unsorted) (Y $$unsorted) (Xa $$unsorted)) (or (not (tptp.less_than (tptp.add (tptp.absolute X) (tptp.absolute Y)) Xa)) (tptp.less_than (tptp.absolute (tptp.add X Y)) Xa))))
% 8.92/9.13  (assume a9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.add (tptp.add X Y) Z) (tptp.add X (tptp.add Y Z)))))
% 8.92/9.13  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))))
% 8.92/9.13  (assume a11 (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))))
% 8.92/9.13  (assume a12 (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))))
% 8.92/9.13  (assume a13 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.minus (tptp.add X Y)) (tptp.add (tptp.minus X) (tptp.minus Y)))))
% 8.92/9.13  (assume a14 (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X)))))
% 8.92/9.13  (assume a15 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X))))
% 8.92/9.13  (assume a16 (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X)))))
% 8.92/9.13  (assume a17 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X))))
% 8.92/9.13  (assume a18 (tptp.less_than tptp.n0 tptp.b))
% 8.92/9.13  (assume a19 (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X))))
% 8.92/9.13  (assume a20 (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b)))))
% 8.92/9.13  (step t1 (cl (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)) :rule or_pos)
% 8.92/9.13  (step t2 (cl (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule reordering :premises (t1))
% 8.92/9.13  (step t3 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) :rule or_pos)
% 8.92/9.13  (step t4 (cl (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))))) :rule reordering :premises (t3))
% 8.92/9.13  (step t5 (cl (not (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b))) :rule or_pos)
% 8.92/9.13  (step t6 (cl (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)) (not (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b))))) :rule reordering :premises (t5))
% 8.92/9.13  (step t7 (cl (=> (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa))))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t8)
% 8.92/9.13  (assume t8.a0 (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))))
% 8.92/9.13  (step t8.t1 (cl (or (not (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa))))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b))))) :rule forall_inst :args ((:= Xa tptp.b)))
% 8.92/9.13  (step t8.t2 (cl (not (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa))))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) :rule or :premises (t8.t1))
% 8.92/9.13  (step t8.t3 (cl (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) :rule resolution :premises (t8.t2 t8.a0))
% 8.92/9.13  (step t8 (cl (not (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa))))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) :rule subproof :discharge (t8.a0))
% 8.92/9.13  (step t9 (cl (=> (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) :rule resolution :premises (t7 t8))
% 8.92/9.13  (step t10 (cl (=> (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) (not (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b))))) :rule implies_neg2)
% 8.92/9.13  (step t11 (cl (=> (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) (=> (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b))))) :rule resolution :premises (t9 t10))
% 8.92/9.13  (step t12 (cl (=> (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa)))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b))))) :rule contraction :premises (t11))
% 8.92/9.13  (step t13 (cl (not (forall ((Xa $$unsorted)) (or (not (tptp.less_than tptp.n0 Xa)) (tptp.less_than tptp.n0 (tptp.half Xa))))) (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) :rule implies :premises (t12))
% 8.92/9.13  (step t14 (cl (or (not (tptp.less_than tptp.n0 tptp.b)) (tptp.less_than tptp.n0 (tptp.half tptp.b)))) :rule resolution :premises (t13 a11))
% 8.92/9.13  (step t15 (cl (tptp.less_than tptp.n0 (tptp.half tptp.b))) :rule resolution :premises (t6 a18 t14))
% 8.92/9.13  (step t16 (cl (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) :rule or_pos)
% 8.92/9.13  (step t17 (cl (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))) (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))))) :rule reordering :premises (t16))
% 8.92/9.13  (step t18 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) :rule or_pos)
% 8.92/9.13  (step t19 (cl (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))) (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))))) :rule reordering :premises (t18))
% 8.92/9.13  (step t20 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) :rule or_pos)
% 8.92/9.13  (step t21 (cl (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))) (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))))) :rule reordering :premises (t20))
% 8.92/9.13  (step t22 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X))))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t23)
% 8.92/9.13  (assume t23.a0 (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X)))))
% 8.92/9.13  (step t23.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))))) :rule forall_inst :args ((:= X (tptp.half tptp.b))))
% 8.92/9.13  (step t23.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) :rule or :premises (t23.t1))
% 8.92/9.13  (step t23.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t23.t2 t23.a0))
% 8.92/9.13  (step t23 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) :rule subproof :discharge (t23.a0))
% 8.92/9.13  (step t24 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t22 t23))
% 8.92/9.13  (step t25 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))))) :rule implies_neg2)
% 8.92/9.13  (step t26 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t24 t25))
% 8.92/9.13  (step t27 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))))) :rule contraction :premises (t26))
% 8.92/9.13  (step t28 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp31 X))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) :rule implies :premises (t27))
% 8.92/9.13  (step t29 (cl (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t28 a14))
% 8.92/9.13  (step t30 (cl (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) :rule resolution :premises (t21 t15 t29))
% 8.92/9.13  (step t31 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) :rule or_pos)
% 8.92/9.13  (step t32 (cl (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))) (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))))) :rule reordering :premises (t31))
% 8.92/9.13  (step t33 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X))))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t34)
% 8.92/9.13  (assume t34.a0 (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X)))))
% 8.92/9.13  (step t34.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))))) :rule forall_inst :args ((:= X (tptp.half tptp.b))))
% 8.92/9.13  (step t34.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) :rule or :premises (t34.t1))
% 8.92/9.13  (step t34.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t34.t2 t34.a0))
% 8.92/9.13  (step t34 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) :rule subproof :discharge (t34.a0))
% 8.92/9.13  (step t35 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t33 t34))
% 8.92/9.13  (step t36 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))))) :rule implies_neg2)
% 8.92/9.13  (step t37 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))))) :rule resolution :premises (t35 t36))
% 8.92/9.13  (step t38 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))))) :rule contraction :premises (t37))
% 8.92/9.13  (step t39 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than tptp.n0 (tptp.fp32 X))))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) :rule implies :premises (t38))
% 8.92/9.13  (step t40 (cl (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t39 a16))
% 8.92/9.13  (step t41 (cl (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) :rule resolution :premises (t32 t15 t40))
% 8.92/9.13  (step t42 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X)))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t43)
% 8.92/9.13  (assume t43.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X))))
% 8.92/9.13  (step t43.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))))) :rule forall_inst :args ((:= X (tptp.fp32 (tptp.half tptp.b))) (:= Y (tptp.fp31 (tptp.half tptp.b)))))
% 8.92/9.13  (step t43.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) :rule or :premises (t43.t1))
% 8.92/9.13  (step t43.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t43.t2 t43.a0))
% 8.92/9.13  (step t43 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) :rule subproof :discharge (t43.a0))
% 8.92/9.13  (step t44 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t42 t43))
% 8.92/9.13  (step t45 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))))) :rule implies_neg2)
% 8.92/9.13  (step t46 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))))) :rule resolution :premises (t44 t45))
% 8.92/9.13  (step t47 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))))) :rule contraction :premises (t46))
% 8.92/9.13  (step t48 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) X)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) :rule implies :premises (t47))
% 8.92/9.13  (step t49 (cl (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t48 a5))
% 8.92/9.13  (step t50 (cl (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) :rule resolution :premises (t19 t30 t41 t49))
% 8.92/9.13  (step t51 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) :rule or_pos)
% 8.92/9.13  (step t52 (cl (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (not (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule reordering :premises (t51))
% 8.92/9.13  (step t53 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) :rule or_pos)
% 8.92/9.13  (step t54 (cl (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule reordering :premises (t53))
% 8.92/9.13  (step t55 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y))))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t56)
% 8.92/9.13  (assume t56.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y)))))
% 8.92/9.13  (step t56.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y))))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule forall_inst :args ((:= X (tptp.fp32 (tptp.half tptp.b))) (:= Y (tptp.fp31 (tptp.half tptp.b)))))
% 8.92/9.13  (step t56.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y))))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule or :premises (t56.t1))
% 8.92/9.13  (step t56.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t56.t2 t56.a0))
% 8.92/9.13  (step t56 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y))))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule subproof :discharge (t56.a0))
% 8.92/9.13  (step t57 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t55 t56))
% 8.92/9.13  (step t58 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule implies_neg2)
% 8.92/9.13  (step t59 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule resolution :premises (t57 t58))
% 8.92/9.13  (step t60 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule contraction :premises (t59))
% 8.92/9.13  (step t61 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than tptp.n0 (tptp.minimum X Y))))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule implies :premises (t60))
% 8.92/9.13  (step t62 (cl (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t61 a4))
% 8.92/9.13  (step t63 (cl (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t54 t30 t41 t62))
% 8.92/9.13  (step t64 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X)))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t65)
% 8.92/9.13  (assume t65.a0 (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X))))
% 8.92/9.13  (step t65.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule forall_inst :args ((:= X (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))
% 8.92/9.13  (step t65.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule or :premises (t65.t1))
% 8.92/9.13  (step t65.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t65.t2 t65.a0))
% 8.92/9.13  (step t65 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule subproof :discharge (t65.a0))
% 8.92/9.13  (step t66 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t64 t65))
% 8.92/9.13  (step t67 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (not (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule implies_neg2)
% 8.92/9.13  (step t68 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule resolution :premises (t66 t67))
% 8.92/9.13  (step t69 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))) :rule contraction :premises (t68))
% 8.92/9.13  (step t70 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 X) (tptp.minus tptp.a))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule implies :premises (t69))
% 8.92/9.13  (step t71 (cl (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t70 a19))
% 8.92/9.13  (step t72 (cl (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t52 t63 t71))
% 8.92/9.13  (step t73 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t74)
% 8.92/9.13  (assume t74.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))))
% 8.92/9.13  (step t74.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))))) :rule forall_inst :args ((:= X (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a)))) (:= Y (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (:= Z (tptp.fp32 (tptp.half tptp.b)))))
% 8.92/9.13  (step t74.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) :rule or :premises (t74.t1))
% 8.92/9.13  (step t74.t3 (cl (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t74.t2 t74.a0))
% 8.92/9.13  (step t74 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) :rule subproof :discharge (t74.a0))
% 8.92/9.13  (step t75 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t73 t74))
% 8.92/9.13  (step t76 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))))) :rule implies_neg2)
% 8.92/9.13  (step t77 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))))) :rule resolution :premises (t75 t76))
% 8.92/9.13  (step t78 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))))) :rule contraction :premises (t77))
% 8.92/9.13  (step t79 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) :rule implies :premises (t78))
% 8.92/9.13  (step t80 (cl (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b))))) :rule resolution :premises (t79 a3))
% 8.92/9.13  (step t81 (cl (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) :rule resolution :premises (t17 t50 t72 t80))
% 8.92/9.13  (step t82 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X)))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t83)
% 8.92/9.13  (assume t83.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X))))
% 8.92/9.13  (step t83.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))))) :rule forall_inst :args ((:= X (tptp.half tptp.b)) (:= Y (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))))
% 8.92/9.13  (step t83.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) :rule or :premises (t83.t1))
% 8.92/9.13  (step t83.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) :rule resolution :premises (t83.t2 t83.a0))
% 8.92/9.13  (step t83 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) :rule subproof :discharge (t83.a0))
% 8.92/9.13  (step t84 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) :rule resolution :premises (t82 t83))
% 8.92/9.13  (step t85 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))))) :rule implies_neg2)
% 8.92/9.13  (step t86 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))))) :rule resolution :premises (t84 t85))
% 8.92/9.13  (step t87 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))))) :rule contraction :premises (t86))
% 8.92/9.13  (step t88 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp32 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g Y) (tptp.minus tptp.l2))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) :rule implies :premises (t87))
% 8.92/9.13  (step t89 (cl (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b)))) :rule resolution :premises (t88 a17))
% 8.92/9.13  (step t90 (cl (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) :rule resolution :premises (t4 t15 t81 t89))
% 8.92/9.13  (step t91 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) :rule or_pos)
% 8.92/9.13  (step t92 (cl (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))))) :rule reordering :premises (t91))
% 8.92/9.13  (step t93 (cl (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) :rule or_pos)
% 8.92/9.13  (step t94 (cl (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))) (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))))) :rule reordering :premises (t93))
% 8.92/9.13  (step t95 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) :rule or_pos)
% 8.92/9.13  (step t96 (cl (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))) (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))))) :rule reordering :premises (t95))
% 8.92/9.13  (step t97 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y)))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t98)
% 8.92/9.13  (assume t98.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y))))
% 8.92/9.13  (step t98.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))))) :rule forall_inst :args ((:= X (tptp.fp32 (tptp.half tptp.b))) (:= Y (tptp.fp31 (tptp.half tptp.b)))))
% 8.92/9.13  (step t98.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) :rule or :premises (t98.t1))
% 8.92/9.13  (step t98.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t98.t2 t98.a0))
% 8.92/9.13  (step t98 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) :rule subproof :discharge (t98.a0))
% 8.92/9.13  (step t99 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t97 t98))
% 8.92/9.13  (step t100 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) (not (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))))) :rule implies_neg2)
% 8.92/9.13  (step t101 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t99 t100))
% 8.92/9.13  (step t102 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))))) :rule contraction :premises (t101))
% 8.92/9.13  (step t103 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than tptp.n0 Y)) (tptp.less_than (tptp.minimum X Y) Y)))) (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) :rule implies :premises (t102))
% 8.92/9.13  (step t104 (cl (or (not (tptp.less_than tptp.n0 (tptp.fp32 (tptp.half tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t103 a6))
% 8.92/9.13  (step t105 (cl (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) :rule resolution :premises (t96 t30 t41 t104))
% 8.92/9.13  (step t106 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t107)
% 8.92/9.13  (assume t107.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))))
% 8.92/9.13  (step t107.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))))) :rule forall_inst :args ((:= X (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a)))) (:= Y (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (:= Z (tptp.fp31 (tptp.half tptp.b)))))
% 8.92/9.13  (step t107.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) :rule or :premises (t107.t1))
% 8.92/9.13  (step t107.t3 (cl (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t107.t2 t107.a0))
% 8.92/9.13  (step t107 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) :rule subproof :discharge (t107.a0))
% 8.92/9.13  (step t108 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t106 t107))
% 8.92/9.13  (step t109 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))))) :rule implies_neg2)
% 8.92/9.13  (step t110 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))))) :rule resolution :premises (t108 t109))
% 8.92/9.13  (step t111 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))))) :rule contraction :premises (t110))
% 8.92/9.13  (step t112 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.less_than X Y)) (not (tptp.less_than Y Z)) (tptp.less_than X Z)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) :rule implies :premises (t111))
% 8.92/9.13  (step t113 (cl (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b))))) :rule resolution :premises (t112 a3))
% 8.92/9.13  (step t114 (cl (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) :rule resolution :premises (t94 t105 t72 t113))
% 8.92/9.13  (step t115 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X)))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t116)
% 8.92/9.13  (assume t116.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X))))
% 8.92/9.13  (step t116.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))))) :rule forall_inst :args ((:= X (tptp.half tptp.b)) (:= Y (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))))))
% 8.92/9.13  (step t116.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) :rule or :premises (t116.t1))
% 8.92/9.13  (step t116.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) :rule resolution :premises (t116.t2 t116.a0))
% 8.92/9.13  (step t116 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) :rule subproof :discharge (t116.a0))
% 8.92/9.13  (step t117 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) :rule resolution :premises (t115 t116))
% 8.92/9.13  (step t118 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) (not (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))))) :rule implies_neg2)
% 8.92/9.13  (step t119 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))))) :rule resolution :premises (t117 t118))
% 8.92/9.13  (step t120 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))))) :rule contraction :premises (t119))
% 8.92/9.13  (step t121 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.absolute (tptp.add Y (tptp.minus tptp.a))) (tptp.fp31 X))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f Y) (tptp.minus tptp.l1))) X)))) (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) :rule implies :premises (t120))
% 8.92/9.13  (step t122 (cl (or (not (tptp.less_than tptp.n0 (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b)))) (tptp.minus tptp.a))) (tptp.fp31 (tptp.half tptp.b)))) (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b)))) :rule resolution :premises (t121 a15))
% 8.92/9.13  (step t123 (cl (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) :rule resolution :premises (t92 t15 t114 t122))
% 8.92/9.13  (step t124 (cl (=> (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa)))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t125)
% 8.92/9.13  (assume t125.a0 (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa))))
% 8.92/9.13  (step t125.t1 (cl (or (not (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule forall_inst :args ((:= X (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1)))) (:= Xa tptp.b) (:= Y (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))))))
% 8.92/9.13  (step t125.t2 (cl (not (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) :rule or :premises (t125.t1))
% 8.92/9.13  (step t125.t3 (cl (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) :rule resolution :premises (t125.t2 t125.a0))
% 8.92/9.13  (step t125 (cl (not (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) :rule subproof :discharge (t125.a0))
% 8.92/9.13  (step t126 (cl (=> (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) :rule resolution :premises (t124 t125))
% 8.92/9.13  (step t127 (cl (=> (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) (not (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule implies_neg2)
% 8.92/9.13  (step t128 (cl (=> (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) (=> (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule resolution :premises (t126 t127))
% 8.92/9.13  (step t129 (cl (=> (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule contraction :premises (t128))
% 8.92/9.13  (step t130 (cl (not (forall ((X $$unsorted) (Xa $$unsorted) (Y $$unsorted)) (or (not (tptp.less_than X (tptp.half Xa))) (not (tptp.less_than Y (tptp.half Xa))) (tptp.less_than (tptp.add X Y) Xa)))) (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) :rule implies :premises (t129))
% 8.92/9.13  (step t131 (cl (or (not (tptp.less_than (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.half tptp.b))) (not (tptp.less_than (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2))) (tptp.half tptp.b))) (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) :rule resolution :premises (t130 a7))
% 8.92/9.13  (step t132 (cl (not (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) :rule or_pos)
% 8.92/9.13  (step t133 (cl (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)) (not (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))))) :rule reordering :premises (t132))
% 8.92/9.13  (step t134 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b))))) :rule implies_neg1)
% 8.92/9.13  (anchor :step t135)
% 8.92/9.13  (assume t135.a0 (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b)))))
% 8.92/9.13  (step t135.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b))))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))))) :rule forall_inst :args ((:= X (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))))
% 8.92/9.13  (step t135.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b))))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule or :premises (t135.t1))
% 8.92/9.13  (step t135.t3 (cl (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule resolution :premises (t135.t2 t135.a0))
% 8.92/9.13  (step t135 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b))))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule subproof :discharge (t135.a0))
% 8.92/9.13  (step t136 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule resolution :premises (t134 t135))
% 8.92/9.13  (step t137 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) (not (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))))) :rule implies_neg2)
% 8.92/9.13  (step t138 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))))) :rule resolution :premises (t136 t137))
% 8.92/9.13  (step t139 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b)))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))))) :rule contraction :premises (t138))
% 8.92/9.13  (step t140 (cl (not (forall ((X $$unsorted)) (or (not (tptp.less_than tptp.n0 X)) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 X)) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 X)) (tptp.minus tptp.l2)))) tptp.b))))) (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule implies :premises (t139))
% 8.92/9.13  (step t141 (cl (or (not (tptp.less_than tptp.n0 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b)))) :rule resolution :premises (t140 a20))
% 8.92/9.13  (step t142 (cl (not (tptp.less_than (tptp.add (tptp.absolute (tptp.add (tptp.f (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l1))) (tptp.absolute (tptp.add (tptp.g (tptp.fp33 (tptp.minimum (tptp.fp32 (tptp.half tptp.b)) (tptp.fp31 (tptp.half tptp.b))))) (tptp.minus tptp.l2)))) tptp.b))) :rule resolution :premises (t133 t63 t141))
% 8.92/9.13  (step t143 (cl) :rule resolution :premises (t2 t90 t123 t131 t142))
% 8.92/9.13  
% 8.92/9.13  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.VZlQZZUoYY/cvc5---1.0.5_13554.smt2
% 8.96/9.14  % cvc5---1.0.5 exiting
% 8.96/9.14  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------