%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW399-1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n020.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 18:19:14 EDT 2024

% Result   : Unsatisfiable 0.21s 0.53s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWW399-1 : TPTP v8.2.0. Released v5.2.0.
% 0.04/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n020.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun May 26 04:57:54 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.53  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.uAop5fYRfr/cvc5---1.0.5_17663.smt2
% 0.21/0.53  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.uAop5fYRfr/cvc5---1.0.5_17663.smt2
% 0.21/0.54  (assume a0 (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))))
% 0.21/0.54  (assume a1 (forall ((X $$unsorted) (Sigma $$unsorted)) (= (tptp.sep (tptp.lseg X X) Sigma) Sigma)))
% 0.21/0.54  (assume a2 (forall ((Y $$unsorted) (Sigma $$unsorted)) (not (tptp.heap (tptp.sep (tptp.next tptp.nil Y) Sigma)))))
% 0.21/0.54  (assume a3 (forall ((Y $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.lseg tptp.nil Y) Sigma))) (= Y tptp.nil))))
% 0.21/0.54  (assume a4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.next X Z) Sigma))))))
% 0.21/0.54  (assume a5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg X Z) Sigma)))) (= X Z))))
% 0.21/0.54  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.lseg X Y) (tptp.sep (tptp.lseg X Z) Sigma)))) (= X Y) (= X Z))))
% 0.21/0.54  (assume a7 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))))
% 0.21/0.54  (assume a8 (forall ((X $$unsorted) (Y $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.lseg X Y) (tptp.sep (tptp.lseg Y tptp.nil) Sigma)))) (tptp.heap (tptp.sep (tptp.lseg X tptp.nil) Sigma)))))
% 0.21/0.54  (assume a9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (W $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.lseg X Y) (tptp.sep (tptp.lseg Y Z) (tptp.sep (tptp.next Z W) Sigma))))) (tptp.heap (tptp.sep (tptp.lseg X Z) (tptp.sep (tptp.next Z W) Sigma))))))
% 0.21/0.54  (assume a10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (W $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.lseg X Y) (tptp.sep (tptp.lseg Y Z) (tptp.sep (tptp.lseg Z W) Sigma))))) (= Z W) (tptp.heap (tptp.sep (tptp.lseg X Z) (tptp.sep (tptp.lseg Z W) Sigma))))))
% 0.21/0.54  (assume a11 (not (= tptp.nil tptp.x1)))
% 0.21/0.54  (assume a12 (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))
% 0.21/0.54  (assume a13 (not (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))
% 0.21/0.54  (step t1 (cl (not (= (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule equiv_pos2)
% 0.21/0.54  (step t2 (cl (= (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) :rule refl)
% 0.21/0.54  (step t3 (cl (= (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule refl)
% 0.21/0.54  (step t4 (cl (= (= (= (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) true) (= (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) :rule equiv_simplify)
% 0.21/0.54  (step t5 (cl (not (= (= (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) true)) (= (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule equiv1 :premises (t4))
% 0.21/0.54  (step t6 (cl (= (= (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))))) :rule all_simplify)
% 0.21/0.54  (step t7 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule refl)
% 0.21/0.54  (step t8 (cl (= (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule all_simplify)
% 0.21/0.54  (step t9 (cl (= (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) :rule cong :premises (t7 t8))
% 0.21/0.54  (step t10 (cl (= (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) true)) :rule all_simplify)
% 0.21/0.54  (step t11 (cl (= (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) true)) :rule trans :premises (t9 t10))
% 0.21/0.54  (step t12 (cl (= (= (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) true)) :rule trans :premises (t6 t11))
% 0.21/0.54  (step t13 (cl (= (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule resolution :premises (t5 t12))
% 0.21/0.54  (step t14 (cl (= (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) :rule cong :premises (t2 t3 t13))
% 0.21/0.54  (step t15 (cl (not (= (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))))) (not (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))))) :rule equiv_pos2)
% 0.21/0.54  (step t16 (cl (= (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))))) :rule refl)
% 0.21/0.54  (step t17 (cl (= (= (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))))) :rule equiv_simplify)
% 0.21/0.54  (step t18 (cl (= (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) (not (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))))) :rule equiv2 :premises (t17))
% 0.21/0.54  (step t19 (cl (not (not (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule not_not)
% 0.21/0.54  (step t20 (cl (= (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule resolution :premises (t18 t19))
% 0.21/0.54  (step t21 (cl (=> (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule implies_neg1)
% 0.21/0.54  (anchor :step t22)
% 0.21/0.54  (assume t22.a0 (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))
% 0.21/0.54  (assume t22.a1 (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))
% 0.21/0.54  (assume t22.a2 (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))
% 0.21/0.54  (step t22.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 0.21/0.54  (step t22.t2 (cl (= (= true false) false)) :rule all_simplify)
% 0.21/0.54  (step t22.t3 (cl (= (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) true) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule equiv_simplify)
% 0.21/0.54  (step t22.t4 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) true) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule equiv2 :premises (t22.t3))
% 0.21/0.54  (step t22.t5 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) true)) :rule resolution :premises (t22.t4 t22.a2))
% 0.21/0.54  (step t22.t6 (cl (= true (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule symm :premises (t22.t5))
% 0.21/0.54  (step t22.t7 (cl (= (tptp.next tptp.x1 tptp.nil) (tptp.next tptp.x1 tptp.nil))) :rule refl)
% 0.21/0.54  (step t22.t8 (cl (= (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp) tptp.emp)) :rule symm :premises (t22.a1))
% 0.21/0.54  (step t22.t9 (cl (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule symm :premises (t22.t8))
% 0.21/0.54  (step t22.t10 (cl (= (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp) (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) :rule cong :premises (t22.t7 t22.t9))
% 0.21/0.54  (step t22.t11 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule cong :premises (t22.t10))
% 0.21/0.54  (step t22.t12 (cl (= (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) false) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) :rule equiv_simplify)
% 0.21/0.54  (step t22.t13 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) false) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) :rule equiv2 :premises (t22.t12))
% 0.21/0.54  (step t22.t14 (cl (not (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) :rule not_not)
% 0.21/0.54  (step t22.t15 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) false) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) :rule resolution :premises (t22.t13 t22.t14))
% 0.21/0.54  (step t22.t16 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) false)) :rule resolution :premises (t22.t15 t22.a0))
% 0.21/0.54  (step t22.t17 (cl (= true false)) :rule trans :premises (t22.t6 t22.t11 t22.t16))
% 0.21/0.54  (step t22.t18 (cl false) :rule resolution :premises (t22.t1 t22.t2 t22.t17))
% 0.21/0.54  (step t22 (cl (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2))
% 0.21/0.54  (step t23 (cl (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule and_pos)
% 0.21/0.54  (step t24 (cl (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule and_pos)
% 0.21/0.54  (step t25 (cl (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) :rule and_pos)
% 0.21/0.54  (step t26 (cl false (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) :rule resolution :premises (t22 t23 t24 t25))
% 0.21/0.54  (step t27 (cl (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) false) :rule reordering :premises (t26))
% 0.21/0.54  (step t28 (cl (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) false) :rule contraction :premises (t27))
% 0.21/0.54  (step t29 (cl (=> (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) false) :rule resolution :premises (t21 t28))
% 0.21/0.54  (step t30 (cl (=> (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) (not false)) :rule implies_neg2)
% 0.21/0.54  (step t31 (cl (=> (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) (=> (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false)) :rule resolution :premises (t29 t30))
% 0.21/0.54  (step t32 (cl (=> (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false)) :rule contraction :premises (t31))
% 0.21/0.54  (step t33 (cl (= (=> (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false) (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))))) :rule implies_simplify)
% 0.21/0.54  (step t34 (cl (not (=> (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false)) (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) :rule equiv1 :premises (t33))
% 0.21/0.54  (step t35 (cl (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) :rule resolution :premises (t32 t34))
% 0.21/0.54  (step t36 (cl (= (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) false)) :rule resolution :premises (t20 t35))
% 0.21/0.54  (step t37 (cl (= (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) false))) :rule cong :premises (t16 t36))
% 0.21/0.54  (step t38 (cl (= (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) false) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))))) :rule all_simplify)
% 0.21/0.54  (step t39 (cl (= (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))))) :rule trans :premises (t37 t38))
% 0.21/0.54  (step t40 (cl (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) :rule implies_neg1)
% 0.21/0.54  (anchor :step t41)
% 0.21/0.54  (assume t41.a0 (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))
% 0.21/0.54  (assume t41.a1 (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))
% 0.21/0.54  (assume t41.a2 (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))
% 0.21/0.54  (step t41.t1 (cl (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule and_neg)
% 0.21/0.54  (step t41.t2 (cl (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule resolution :premises (t41.t1 t41.a2 t41.a1 t41.a0))
% 0.21/0.54  (step t41 (cl (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule subproof :discharge (t41.a0 t41.a1 t41.a2))
% 0.21/0.54  (step t42 (cl (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) :rule and_pos)
% 0.21/0.54  (step t43 (cl (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule and_pos)
% 0.21/0.54  (step t44 (cl (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule and_pos)
% 0.21/0.54  (step t45 (cl (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))))) :rule resolution :premises (t41 t42 t43 t44))
% 0.21/0.54  (step t46 (cl (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule reordering :premises (t45))
% 0.21/0.54  (step t47 (cl (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule contraction :premises (t46))
% 0.21/0.54  (step t48 (cl (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) :rule resolution :premises (t40 t47))
% 0.21/0.54  (step t49 (cl (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (not (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) :rule implies_neg2)
% 0.21/0.54  (step t50 (cl (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)))) (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) :rule resolution :premises (t48 t49))
% 0.21/0.54  (step t51 (cl (=> (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) (and (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) :rule contraction :premises (t50))
% 0.21/0.54  (step t52 (cl (not (and (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp)) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))))) :rule resolution :premises (t15 t39 t51))
% 0.21/0.54  (step t53 (cl (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) :rule not_and :premises (t52))
% 0.21/0.54  (step t54 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))))) :rule or_neg)
% 0.21/0.54  (step t55 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule or_neg)
% 0.21/0.54  (step t56 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (not (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))))) :rule or_neg)
% 0.21/0.54  (step t57 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))))) :rule resolution :premises (t53 t54 t55 t56))
% 0.21/0.54  (step t58 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))))) :rule contraction :premises (t57))
% 0.21/0.54  (step t59 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule resolution :premises (t1 t14 t58))
% 0.21/0.54  (step t60 (cl (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) :rule or :premises (t59))
% 0.21/0.54  (step t61 (cl (not (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))) :rule or_pos)
% 0.21/0.54  (step t62 (cl (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (not (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) :rule reordering :premises (t61))
% 0.21/0.54  (step t63 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) :rule equiv_pos2)
% 0.21/0.54  (step t64 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))))) :rule refl)
% 0.21/0.54  (step t65 (cl (= (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))))) :rule refl)
% 0.21/0.54  (step t66 (cl (= (= tptp.x1 tptp.nil) (= tptp.nil tptp.x1))) :rule all_simplify)
% 0.21/0.54  (step t67 (cl (= (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) :rule refl)
% 0.21/0.54  (step t68 (cl (= (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) :rule cong :premises (t65 t66 t67))
% 0.21/0.54  (step t69 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))))) :rule cong :premises (t64 t68))
% 0.21/0.54  (step t70 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma))))) :rule implies_neg1)
% 0.21/0.54  (anchor :step t71)
% 0.21/0.54  (assume t71.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))))
% 0.21/0.54  (step t71.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) :rule forall_inst :args ((:= X tptp.x1) (:= Y tptp.nil) (:= Z tptp.nil) (:= Sigma tptp.emp)))
% 0.21/0.54  (step t71.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) :rule or :premises (t71.t1))
% 0.21/0.54  (step t71.t3 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) :rule resolution :premises (t71.t2 t71.a0))
% 0.21/0.54  (step t71 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) :rule subproof :discharge (t71.a0))
% 0.21/0.54  (step t72 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) :rule resolution :premises (t70 t71))
% 0.21/0.54  (step t73 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) (not (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) :rule implies_neg2)
% 0.21/0.54  (step t74 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) :rule resolution :premises (t72 t73))
% 0.21/0.54  (step t75 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.x1 tptp.nil) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) :rule contraction :premises (t74))
% 0.21/0.54  (step t76 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp))))) :rule resolution :premises (t63 t69 t75))
% 0.21/0.54  (step t77 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma))))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) :rule implies :premises (t76))
% 0.21/0.54  (step t78 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) (= tptp.nil tptp.x1) (tptp.heap (tptp.sep (tptp.lseg tptp.x1 tptp.nil) tptp.emp)))) :rule resolution :premises (t77 a7))
% 0.21/0.54  (step t79 (cl (not (tptp.heap (tptp.sep (tptp.next tptp.x1 tptp.nil) (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))))) :rule resolution :premises (t62 a11 a13 t78))
% 0.21/0.54  (step t80 (cl (=> (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma)))) :rule implies_neg1)
% 0.21/0.54  (anchor :step t81)
% 0.21/0.54  (assume t81.a0 (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))))
% 0.21/0.54  (step t81.t1 (cl (or (not (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) :rule forall_inst :args ((:= X tptp.nil) (:= Sigma tptp.emp)))
% 0.21/0.54  (step t81.t2 (cl (not (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule or :premises (t81.t1))
% 0.21/0.54  (step t81.t3 (cl (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule resolution :premises (t81.t2 t81.a0))
% 0.21/0.54  (step t81 (cl (not (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule subproof :discharge (t81.a0))
% 0.21/0.54  (step t82 (cl (=> (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule resolution :premises (t80 t81))
% 0.21/0.54  (step t83 (cl (=> (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (not (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) :rule implies_neg2)
% 0.21/0.54  (step t84 (cl (=> (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) (=> (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) :rule resolution :premises (t82 t83))
% 0.21/0.54  (step t85 (cl (=> (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp)))) :rule contraction :premises (t84))
% 0.21/0.54  (step t86 (cl (not (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma)))) (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule implies :premises (t85))
% 0.21/0.54  (step t87 (cl (not (= (forall ((X $$unsorted) (Sigma $$unsorted)) (= (tptp.sep (tptp.lseg X X) Sigma) Sigma)) (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))))) (not (forall ((X $$unsorted) (Sigma $$unsorted)) (= (tptp.sep (tptp.lseg X X) Sigma) Sigma))) (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma)))) :rule equiv_pos2)
% 0.21/0.54  (anchor :step t88 :args ((X $$unsorted) (:= X X) (Sigma $$unsorted) (:= Sigma Sigma)))
% 0.21/0.54  (step t88.t1 (cl (= X X)) :rule refl)
% 0.21/0.54  (step t88.t2 (cl (= Sigma Sigma)) :rule refl)
% 0.21/0.54  (step t88.t3 (cl (= (= (tptp.sep (tptp.lseg X X) Sigma) Sigma) (= Sigma (tptp.sep (tptp.lseg X X) Sigma)))) :rule all_simplify)
% 0.21/0.54  (step t88 (cl (= (forall ((X $$unsorted) (Sigma $$unsorted)) (= (tptp.sep (tptp.lseg X X) Sigma) Sigma)) (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma))))) :rule bind)
% 0.21/0.54  (step t89 (cl (forall ((X $$unsorted) (Sigma $$unsorted)) (= Sigma (tptp.sep (tptp.lseg X X) Sigma)))) :rule resolution :premises (t87 t88 a1))
% 0.21/0.54  (step t90 (cl (= tptp.emp (tptp.sep (tptp.lseg tptp.nil tptp.nil) tptp.emp))) :rule resolution :premises (t86 t89))
% 0.21/0.54  (step t91 (cl) :rule resolution :premises (t60 t79 t90 a12))
% 0.21/0.54  
% 0.21/0.54  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.uAop5fYRfr/cvc5---1.0.5_17663.smt2
% 0.21/0.54  % cvc5---1.0.5 exiting
% 0.21/0.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------