TSTP Solution File: GRP148-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP148-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n023.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 16:53:26 EDT 2024
% Result : Unsatisfiable 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP148-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 26 17:31:09 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.7EQAsnNMoN/cvc5---1.0.5_31330.smt2
% 0.20/0.53 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.7EQAsnNMoN/cvc5---1.0.5_31330.smt2
% 0.20/0.53 (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 0.20/0.53 (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 0.20/0.53 (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 0.20/0.53 (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 0.20/0.53 (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 0.20/0.53 (assume a5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 0.20/0.53 (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 0.20/0.53 (assume a7 (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)))
% 0.20/0.53 (assume a8 (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)))
% 0.20/0.53 (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)))
% 0.20/0.53 (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)))
% 0.20/0.53 (assume a11 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 0.20/0.53 (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 0.20/0.53 (assume a13 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 0.20/0.53 (assume a14 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 0.20/0.53 (assume a15 (= (tptp.least_upper_bound tptp.a tptp.c) tptp.c))
% 0.20/0.53 (assume a16 (= (tptp.least_upper_bound tptp.b tptp.c) tptp.c))
% 0.20/0.53 (assume a17 (not (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c) (tptp.least_upper_bound tptp.a tptp.b))))
% 0.20/0.53 (step t1 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t2)
% 0.20/0.53 (assume t2.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 0.20/0.53 (step t2.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.b)) (:= Y tptp.c)))
% 0.20/0.53 (step t2.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule or :premises (t2.t1))
% 0.20/0.53 (step t2.t3 (cl (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule resolution :premises (t2.t2 t2.a0))
% 0.20/0.53 (step t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule subproof :discharge (t2.a0))
% 0.20/0.53 (step t3 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule resolution :premises (t1 t2))
% 0.20/0.53 (step t4 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule implies_neg2)
% 0.20/0.53 (step t5 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t3 t4))
% 0.20/0.53 (step t6 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule contraction :premises (t5))
% 0.20/0.53 (step t7 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule implies :premises (t6))
% 0.20/0.53 (step t8 (cl (not (= (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))))) (not (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule equiv_pos2)
% 0.20/0.53 (step t9 (cl (= (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))))) :rule refl)
% 0.20/0.53 (step t10 (cl (= (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))))) :rule refl)
% 0.20/0.53 (step t11 (cl (= (= (= (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) true) (= (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule equiv_simplify)
% 0.20/0.53 (step t12 (cl (not (= (= (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) true)) (= (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule equiv1 :premises (t11))
% 0.20/0.53 (step t13 (cl (= (= (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))))) :rule all_simplify)
% 0.20/0.53 (step t14 (cl (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule refl)
% 0.20/0.53 (step t15 (cl (= (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule all_simplify)
% 0.20/0.53 (step t16 (cl (= (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule cong :premises (t14 t15))
% 0.20/0.53 (step t17 (cl (= (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) true)) :rule all_simplify)
% 0.20/0.53 (step t18 (cl (= (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) true)) :rule trans :premises (t16 t17))
% 0.20/0.53 (step t19 (cl (= (= (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) true)) :rule trans :premises (t13 t18))
% 0.20/0.53 (step t20 (cl (= (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule resolution :premises (t12 t19))
% 0.20/0.53 (step t21 (cl (= (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule refl)
% 0.20/0.53 (step t22 (cl (= (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule refl)
% 0.20/0.53 (step t23 (cl (= (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))))) :rule cong :premises (t9 t10 t20 t21 t22))
% 0.20/0.53 (step t24 (cl (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule and_neg)
% 0.20/0.53 (step t25 (cl (=> (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t26)
% 0.20/0.53 (assume t26.a0 (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)))
% 0.20/0.53 (assume t26.a1 (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)))
% 0.20/0.53 (assume t26.a2 (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))
% 0.20/0.53 (assume t26.a3 (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))
% 0.20/0.53 (step t26.t1 (cl (=> (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t26.t2)
% 0.20/0.53 (assume t26.t2.a0 (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))
% 0.20/0.53 (assume t26.t2.a1 (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)))
% 0.20/0.53 (assume t26.t2.a2 (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)))
% 0.20/0.53 (assume t26.t2.a3 (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))
% 0.20/0.53 (step t26.t2.t1 (cl (= (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) false) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule equiv_simplify)
% 0.20/0.53 (step t26.t2.t2 (cl (not (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) false)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule equiv1 :premises (t26.t2.t1))
% 0.20/0.53 (step t26.t2.t3 (cl (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound tptp.a tptp.b))) :rule refl)
% 0.20/0.53 (step t26.t2.t4 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c) (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)))) :rule symm :premises (t26.t2.a3))
% 0.20/0.53 (step t26.t2.t5 (cl (= tptp.a tptp.a)) :rule refl)
% 0.20/0.53 (step t26.t2.t6 (cl (= (tptp.least_upper_bound tptp.b tptp.c) tptp.c)) :rule symm :premises (t26.t2.a2))
% 0.20/0.53 (step t26.t2.t7 (cl (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) :rule cong :premises (t26.t2.t5 t26.t2.t6))
% 0.20/0.53 (step t26.t2.t8 (cl (= (tptp.least_upper_bound tptp.a tptp.c) tptp.c)) :rule symm :premises (t26.t2.a1))
% 0.20/0.53 (step t26.t2.t9 (cl (= (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c) tptp.c)) :rule trans :premises (t26.t2.t4 t26.t2.t7 t26.t2.t8))
% 0.20/0.53 (step t26.t2.t10 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule cong :premises (t26.t2.t3 t26.t2.t9))
% 0.20/0.53 (step t26.t2.t11 (cl (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule cong :premises (t26.t2.t3 t26.t2.t10))
% 0.20/0.53 (step t26.t2.t12 (cl (= (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) false) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule equiv_simplify)
% 0.20/0.53 (step t26.t2.t13 (cl (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) false) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule equiv2 :premises (t26.t2.t12))
% 0.20/0.53 (step t26.t2.t14 (cl (not (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule not_not)
% 0.20/0.53 (step t26.t2.t15 (cl (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) false) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule resolution :premises (t26.t2.t13 t26.t2.t14))
% 0.20/0.53 (step t26.t2.t16 (cl (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) false)) :rule resolution :premises (t26.t2.t15 t26.t2.a0))
% 0.20/0.53 (step t26.t2.t17 (cl (= (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) false)) :rule trans :premises (t26.t2.t11 t26.t2.t16))
% 0.20/0.53 (step t26.t2.t18 (cl (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t26.t2.t2 t26.t2.t17))
% 0.20/0.53 (step t26.t2 (cl (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule subproof :discharge (t26.t2.a0 t26.t2.a1 t26.t2.a2 t26.t2.a3))
% 0.20/0.53 (step t26.t3 (cl (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule and_pos)
% 0.20/0.53 (step t26.t4 (cl (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) :rule and_pos)
% 0.20/0.53 (step t26.t5 (cl (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) :rule and_pos)
% 0.20/0.53 (step t26.t6 (cl (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule and_pos)
% 0.20/0.53 (step t26.t7 (cl (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t26.t2 t26.t3 t26.t4 t26.t5 t26.t6))
% 0.20/0.53 (step t26.t8 (cl (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule reordering :premises (t26.t7))
% 0.20/0.53 (step t26.t9 (cl (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule contraction :premises (t26.t8))
% 0.20/0.53 (step t26.t10 (cl (=> (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t26.t1 t26.t9))
% 0.20/0.53 (step t26.t11 (cl (=> (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule implies_neg2)
% 0.20/0.53 (step t26.t12 (cl (=> (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (=> (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule resolution :premises (t26.t10 t26.t11))
% 0.20/0.53 (step t26.t13 (cl (=> (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule contraction :premises (t26.t12))
% 0.20/0.53 (step t26.t14 (cl (not (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule implies :premises (t26.t13))
% 0.20/0.53 (step t26.t15 (cl (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule and_neg)
% 0.20/0.53 (step t26.t16 (cl (and (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule resolution :premises (t26.t15 t26.a2 t26.a0 t26.a1 t26.a3))
% 0.20/0.53 (step t26.t17 (cl (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t26.t14 t26.t16))
% 0.20/0.53 (step t26 (cl (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule subproof :discharge (t26.a0 t26.a1 t26.a2 t26.a3))
% 0.20/0.53 (step t27 (cl (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) :rule and_pos)
% 0.20/0.53 (step t28 (cl (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) :rule and_pos)
% 0.20/0.53 (step t29 (cl (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule and_pos)
% 0.20/0.53 (step t30 (cl (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule and_pos)
% 0.20/0.53 (step t31 (cl (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t26 t27 t28 t29 t30))
% 0.20/0.53 (step t32 (cl (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule reordering :premises (t31))
% 0.20/0.53 (step t33 (cl (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule contraction :premises (t32))
% 0.20/0.53 (step t34 (cl (=> (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t25 t33))
% 0.20/0.53 (step t35 (cl (=> (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule implies_neg2)
% 0.20/0.53 (step t36 (cl (=> (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (=> (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule resolution :premises (t34 t35))
% 0.20/0.53 (step t37 (cl (=> (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule contraction :premises (t36))
% 0.20/0.53 (step t38 (cl (not (and (= tptp.c (tptp.least_upper_bound tptp.a tptp.c)) (= tptp.c (tptp.least_upper_bound tptp.b tptp.c)) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule implies :premises (t37))
% 0.20/0.53 (step t39 (cl (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t24 t38))
% 0.20/0.53 (step t40 (cl (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))))) :rule or_neg)
% 0.20/0.53 (step t41 (cl (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))))) :rule or_neg)
% 0.20/0.53 (step t42 (cl (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule or_neg)
% 0.20/0.53 (step t43 (cl (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule or_neg)
% 0.20/0.53 (step t44 (cl (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule or_neg)
% 0.20/0.53 (step t45 (cl (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule resolution :premises (t39 t40 t41 t42 t43 t44))
% 0.20/0.53 (step t46 (cl (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule contraction :premises (t45))
% 0.20/0.53 (step t47 (cl (or (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))))) :rule resolution :premises (t8 t23 t46))
% 0.20/0.53 (step t48 (cl (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule or :premises (t47))
% 0.20/0.53 (step t49 (cl (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)) (not (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) (not (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule reordering :premises (t48))
% 0.20/0.53 (step t50 (cl (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule not_symm :premises (a17))
% 0.20/0.53 (step t51 (cl (= tptp.c (tptp.least_upper_bound tptp.a tptp.c))) :rule symm :premises (a15))
% 0.20/0.53 (step t52 (cl (= tptp.c (tptp.least_upper_bound tptp.b tptp.c))) :rule symm :premises (a16))
% 0.20/0.53 (step t53 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t54)
% 0.20/0.53 (assume t54.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 0.20/0.53 (step t54.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.b) (:= Z tptp.c)))
% 0.20/0.53 (step t54.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule or :premises (t54.t1))
% 0.20/0.53 (step t54.t3 (cl (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule resolution :premises (t54.t2 t54.a0))
% 0.20/0.53 (step t54 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule subproof :discharge (t54.a0))
% 0.20/0.53 (step t55 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule resolution :premises (t53 t54))
% 0.20/0.53 (step t56 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (not (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule implies_neg2)
% 0.20/0.53 (step t57 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule resolution :premises (t55 t56))
% 0.20/0.53 (step t58 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c)))) :rule contraction :premises (t57))
% 0.20/0.53 (step t59 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z)))) (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule implies :premises (t58))
% 0.20/0.53 (step t60 (cl (= (tptp.least_upper_bound tptp.a (tptp.least_upper_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))) :rule resolution :premises (t59 a6))
% 0.20/0.53 (step t61 (cl (not (= (tptp.least_upper_bound tptp.a tptp.b) (tptp.greatest_lower_bound (tptp.least_upper_bound tptp.a tptp.b) (tptp.least_upper_bound (tptp.least_upper_bound tptp.a tptp.b) tptp.c))))) :rule resolution :premises (t49 t50 t51 t52 t60))
% 0.20/0.53 (step t62 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule equiv_pos2)
% 0.20/0.53 (anchor :step t63 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.20/0.53 (step t63.t1 (cl (= X X)) :rule refl)
% 0.20/0.53 (step t63.t2 (cl (= Y Y)) :rule refl)
% 0.20/0.53 (step t63.t3 (cl (= (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule all_simplify)
% 0.20/0.53 (step t63 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))) :rule bind)
% 0.20/0.53 (step t64 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule resolution :premises (t62 t63 a10))
% 0.20/0.53 (step t65 (cl) :rule resolution :premises (t7 t61 t64))
% 0.20/0.53
% 0.20/0.53 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.7EQAsnNMoN/cvc5---1.0.5_31330.smt2
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.20/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------