TSTP Solution File: SWW413-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW413-1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n024.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 18:19:16 EDT 2024
% Result : Unsatisfiable 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW413-1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n024.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
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun May 26 06:29:24 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.20/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.uERVxEtZQ7/cvc5---1.0.5_15293.smt2
% 0.20/0.54 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.uERVxEtZQ7/cvc5---1.0.5_15293.smt2
% 0.20/0.54 (assume a0 (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))))
% 0.20/0.54 (assume a1 (forall ((X $$unsorted) (Sigma $$unsorted)) (= (tptp.sep (tptp.lseg X X) Sigma) Sigma)))
% 0.20/0.54 (assume a2 (forall ((Y $$unsorted) (Sigma $$unsorted)) (not (tptp.heap (tptp.sep (tptp.next tptp.nil Y) Sigma)))))
% 0.20/0.54 (assume a3 (forall ((Y $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.lseg tptp.nil Y) Sigma))) (= Y tptp.nil))))
% 0.20/0.54 (assume a4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.next X Z) Sigma))))))
% 0.20/0.54 (assume a5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg X Z) Sigma)))) (= X Z))))
% 0.20/0.54 (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.lseg X Y) (tptp.sep (tptp.lseg X Z) Sigma)))) (= X Y) (= X Z))))
% 0.20/0.54 (assume a7 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.next X Y) (tptp.sep (tptp.lseg Y Z) Sigma)))) (= X Y) (tptp.heap (tptp.sep (tptp.lseg X Z) Sigma)))))
% 0.20/0.54 (assume a8 (forall ((X $$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)))))
% 0.20/0.54 (assume a9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (W $$unsorted) (Sigma $$unsorted)) (or (not (tptp.heap (tptp.sep (tptp.lseg X Y) (tptp.sep (tptp.lseg Y Z) (tptp.sep (tptp.next Z W) Sigma))))) (tptp.heap (tptp.sep (tptp.lseg X Z) (tptp.sep (tptp.next Z W) Sigma))))))
% 0.20/0.54 (assume a10 (forall ((X $$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))))))
% 0.20/0.54 (assume a11 (not (= tptp.nil tptp.x1)))
% 0.20/0.54 (assume a12 (not (= tptp.nil tptp.x2)))
% 0.20/0.54 (assume a13 (not (= tptp.x3 tptp.x2)))
% 0.20/0.54 (assume a14 (not (= tptp.x4 tptp.x1)))
% 0.20/0.54 (assume a15 (not (= tptp.x4 tptp.x2)))
% 0.20/0.54 (assume a16 (not (= tptp.x1 tptp.x2)))
% 0.20/0.54 (assume a17 (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))
% 0.20/0.54 (assume a18 (not (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp))))
% 0.20/0.54 (step t1 (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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 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)
% 0.20/0.54 (anchor :step t2)
% 0.20/0.54 (assume t2.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)))))
% 0.20/0.54 (step t2.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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp))))) :rule forall_inst :args ((:= X tptp.x2) (:= Y tptp.x3) (:= Z tptp.nil) (:= Sigma tptp.emp)))
% 0.20/0.54 (step t2.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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)))) :rule or :premises (t2.t1))
% 0.20/0.54 (step t2.t3 (cl (or (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)))) :rule resolution :premises (t2.t2 t2.a0))
% 0.20/0.54 (step 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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)))) :rule subproof :discharge (t2.a0))
% 0.20/0.54 (step t3 (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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)))) (or (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)))) :rule resolution :premises (t1 t2))
% 0.20/0.54 (step t4 (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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)))) (not (or (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp))))) :rule implies_neg2)
% 0.20/0.54 (step t5 (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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp))))) :rule resolution :premises (t3 t4))
% 0.20/0.54 (step t6 (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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp))))) :rule contraction :premises (t5))
% 0.20/0.54 (step t7 (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.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)))) :rule implies :premises (t6))
% 0.20/0.54 (step t8 (cl (not (or (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)))) (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp))) :rule or_pos)
% 0.20/0.54 (step t9 (cl (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp)) (= tptp.x2 tptp.x3) (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (not (or (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp))))) :rule reordering :premises (t8))
% 0.20/0.54 (step t10 (cl (not (= tptp.x2 tptp.x3))) :rule not_symm :premises (a13))
% 0.20/0.54 (step t11 (cl (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (not (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (not (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule and_neg)
% 0.20/0.54 (step t12 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t13)
% 0.20/0.54 (assume t13.a0 (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))
% 0.20/0.54 (assume t13.a1 (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))
% 0.20/0.54 (step t13.t1 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t13.t2)
% 0.20/0.54 (assume t13.t2.a0 (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))
% 0.20/0.54 (assume t13.t2.a1 (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))
% 0.20/0.54 (step t13.t2.t1 (cl (= (= (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))) true) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule equiv_simplify)
% 0.20/0.54 (step t13.t2.t2 (cl (not (= (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))) true)) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule equiv1 :premises (t13.t2.t1))
% 0.20/0.54 (step t13.t2.t3 (cl (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) :rule symm :premises (t13.t2.a1))
% 0.20/0.54 (step t13.t2.t4 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))) (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))) :rule cong :premises (t13.t2.t3))
% 0.20/0.54 (step t13.t2.t5 (cl (= (= (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) true) (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))) :rule equiv_simplify)
% 0.20/0.54 (step t13.t2.t6 (cl (= (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) true) (not (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))) :rule equiv2 :premises (t13.t2.t5))
% 0.20/0.54 (step t13.t2.t7 (cl (= (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) true)) :rule resolution :premises (t13.t2.t6 t13.t2.a0))
% 0.20/0.54 (step t13.t2.t8 (cl (= (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))) true)) :rule trans :premises (t13.t2.t4 t13.t2.t7))
% 0.20/0.54 (step t13.t2.t9 (cl (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule resolution :premises (t13.t2.t2 t13.t2.t8))
% 0.20/0.54 (step t13.t2 (cl (not (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (not (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule subproof :discharge (t13.t2.a0 t13.t2.a1))
% 0.20/0.54 (step t13.t3 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) :rule and_pos)
% 0.20/0.54 (step t13.t4 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule and_pos)
% 0.20/0.54 (step t13.t5 (cl (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))) (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))))) :rule resolution :premises (t13.t2 t13.t3 t13.t4))
% 0.20/0.54 (step t13.t6 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule reordering :premises (t13.t5))
% 0.20/0.54 (step t13.t7 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule contraction :premises (t13.t6))
% 0.20/0.54 (step t13.t8 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule resolution :premises (t13.t1 t13.t7))
% 0.20/0.54 (step t13.t9 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule implies_neg2)
% 0.20/0.54 (step t13.t10 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule resolution :premises (t13.t8 t13.t9))
% 0.20/0.54 (step t13.t11 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule contraction :premises (t13.t10))
% 0.20/0.54 (step t13.t12 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule implies :premises (t13.t11))
% 0.20/0.54 (step t13.t13 (cl (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (not (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (not (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule and_neg)
% 0.20/0.54 (step t13.t14 (cl (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule resolution :premises (t13.t13 t13.a0 t13.a1))
% 0.20/0.54 (step t13.t15 (cl (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule resolution :premises (t13.t12 t13.t14))
% 0.20/0.54 (step t13 (cl (not (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (not (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule subproof :discharge (t13.a0 t13.a1))
% 0.20/0.54 (step t14 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) :rule and_pos)
% 0.20/0.54 (step t15 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule and_pos)
% 0.20/0.54 (step t16 (cl (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))) (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))))) :rule resolution :premises (t13 t14 t15))
% 0.20/0.54 (step t17 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule reordering :premises (t16))
% 0.20/0.54 (step t18 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule contraction :premises (t17))
% 0.20/0.54 (step t19 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule resolution :premises (t12 t18))
% 0.20/0.54 (step t20 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule implies_neg2)
% 0.20/0.54 (step t21 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule resolution :premises (t19 t20))
% 0.20/0.54 (step t22 (cl (=> (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule contraction :premises (t21))
% 0.20/0.54 (step t23 (cl (not (and (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule implies :premises (t22))
% 0.20/0.54 (step t24 (cl (not (tptp.heap (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (not (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule resolution :premises (t11 t23))
% 0.20/0.54 (step t25 (cl (not (= (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))))) (not (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))) (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule equiv_pos2)
% 0.20/0.54 (step t26 (cl (= (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))))) :rule refl)
% 0.20/0.54 (step t27 (cl (= (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule all_simplify)
% 0.20/0.54 (step t28 (cl (= (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))))) :rule cong :premises (t26 t27))
% 0.20/0.54 (step t29 (cl (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma))))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t30)
% 0.20/0.54 (assume t30.a0 (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))))
% 0.20/0.54 (step t30.t1 (cl (or (not (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma))))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))) :rule forall_inst :args ((:= S (tptp.next tptp.x2 tptp.x3)) (:= T (tptp.lseg tptp.x3 tptp.nil)) (:= Sigma tptp.emp)))
% 0.20/0.54 (step t30.t2 (cl (not (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma))))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) :rule or :premises (t30.t1))
% 0.20/0.54 (step t30.t3 (cl (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) :rule resolution :premises (t30.t2 t30.a0))
% 0.20/0.54 (step t30 (cl (not (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma))))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) :rule subproof :discharge (t30.a0))
% 0.20/0.54 (step t31 (cl (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) :rule resolution :premises (t29 t30))
% 0.20/0.54 (step t32 (cl (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (not (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))) :rule implies_neg2)
% 0.20/0.54 (step t33 (cl (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)))) (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))) :rule resolution :premises (t31 t32))
% 0.20/0.54 (step t34 (cl (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp))))) :rule contraction :premises (t33))
% 0.20/0.54 (step t35 (cl (=> (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma)))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp))))) :rule resolution :premises (t25 t28 t34))
% 0.20/0.54 (step t36 (cl (not (forall ((S $$unsorted) (T $$unsorted) (Sigma $$unsorted)) (= (tptp.sep S (tptp.sep T Sigma)) (tptp.sep T (tptp.sep S Sigma))))) (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule implies :premises (t35))
% 0.20/0.54 (step t37 (cl (= (tptp.sep (tptp.lseg tptp.x3 tptp.nil) (tptp.sep (tptp.next tptp.x2 tptp.x3) tptp.emp)) (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule resolution :premises (t36 a0))
% 0.20/0.54 (step t38 (cl (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) :rule resolution :premises (t24 a17 t37))
% 0.20/0.54 (step t39 (cl (not (or (not (tptp.heap (tptp.sep (tptp.next tptp.x2 tptp.x3) (tptp.sep (tptp.lseg tptp.x3 tptp.nil) tptp.emp)))) (= tptp.x2 tptp.x3) (tptp.heap (tptp.sep (tptp.lseg tptp.x2 tptp.nil) tptp.emp))))) :rule resolution :premises (t9 a18 t10 t38))
% 0.20/0.54 (step t40 (cl) :rule resolution :premises (t7 t39 a7))
% 0.20/0.54
% 0.20/0.54 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.uERVxEtZQ7/cvc5---1.0.5_15293.smt2
% 0.35/0.55 % cvc5---1.0.5 exiting
% 0.35/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------