%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:26 AM UTC 2026
% Result : Unsatisfiable 2.58s 1.17s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 34 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X3,X0,X1] : ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f3,plain,
! [X2,X3,X0,X1] : true = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true),true),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : ifeq(c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X1,X0,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
fof(f5,plain,
! [X2,X3,X0,X1] : true = ifeq(c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X1,X0,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X2,X0,X1] : ifeq(c_in(X0,X1,tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
fof(f7,plain,
! [X2,X0,X1] : true = ifeq(c_in(X0,X1,tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] : ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
fof(f9,plain,
! [X2,X3,X0,X1] : true = ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f11,plain,
! [X2,X0,X1] : true = c_in(X0,c_insert(X0,X1,X2),X2),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f13,plain,
true = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f15,plain,
true = c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f17,plain,
true != c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(reorient_equations,[],[f16]) ).
fof(f20,plain,
! [X2,X0,X1] : true = ifeq(true,true,c_in(X0,c_PropLog_Othms(c_insert(X0,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),
inference(superposition,[],[f7,f11]) ).
fof(f23,plain,
! [X2,X0,X1] : true = c_in(X0,c_PropLog_Othms(c_insert(X0,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),
inference(forward_demodulation,[],[f20,f1]) ).
fof(f34,plain,
! [X0] : true = ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(superposition,[],[f9,f13]) ).
fof(f35,plain,
! [X0] : true = ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(superposition,[],[f9,f15]) ).
fof(f40,plain,
! [X0] : true = c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[],[f35,f1]) ).
fof(f41,plain,
! [X0] : true = c_in(v_p,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[],[f34,f1]) ).
fof(f126,plain,
! [X0] : true = ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),
inference(superposition,[],[f3,f40]) ).
fof(f138,plain,
! [X0,X1] : true = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(true,true,c_in(X0,c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),
inference(superposition,[],[f3,f41]) ).
fof(f160,plain,
! [X0,X1] : true = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X0,c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(forward_demodulation,[],[f138,f1]) ).
fof(f172,plain,
! [X0] : true = ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(forward_demodulation,[],[f126,f1]) ).
fof(f1012,plain,
! [X0] : true = ifeq(true,true,c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(superposition,[],[f160,f23]) ).
fof(f1022,plain,
! [X0] : true = c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[],[f1012,f1]) ).
fof(f1032,plain,
true = ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(superposition,[],[f172,f1022]) ).
fof(f1046,plain,
true = c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[],[f1032,f1]) ).
fof(f1067,plain,
true = ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),
inference(superposition,[],[f5,f1046]) ).
fof(f1078,plain,
true = c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[],[f1067,f1]) ).
fof(f1079,plain,
$false,
inference(forward_subsumption_resolution,[],[f1078,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n017.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 15:38:50 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.58/1.17 % (2756582)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.58/1.17 % (2756667)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=266514730:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.58/1.17 % (2756667)First to succeed.
% 2.58/1.17 % (2756667)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2756582"
% 2.58/1.17 % (2756662)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1665335068:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.58/1.17 % (2756665)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3867692567:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.58/1.17 % (2756664)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=406288382:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.58/1.17 % (2756666)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2648405673:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.58/1.17 % (2756663)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2685456790:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.58/1.17 % (2756661)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=25733619:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.58/1.17 % (2756664)Instruction limit reached!
% 2.58/1.17 % (2756664)------------------------------
% 2.58/1.17 % (2756664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.17 % (2756664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.17 % (2756664)CaDiCaL version: 2.1.3
% 2.58/1.17 % (2756664)Termination reason: Instruction limit
% 2.58/1.17 % (2756664)Termination phase: Saturation
% 2.58/1.17 % (2756664)Time elapsed: 0.080 s
% 2.58/1.17 % (2756664)Peak memory usage: 88 MB
% 2.58/1.17 % (2756664)Instructions burned: 137 (million)
% 2.58/1.17 % (2756665)Instruction limit reached!
% 2.58/1.17 % (2756665)------------------------------
% 2.58/1.17 % (2756665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.17 % (2756665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.17 % (2756665)CaDiCaL version: 2.1.3
% 2.58/1.17 % (2756665)Termination reason: Instruction limit
% 2.58/1.17 % (2756665)Termination phase: Saturation
% 2.58/1.17 % (2756665)Time elapsed: 0.104 s
% 2.58/1.17 % (2756665)Peak memory usage: 89 MB
% 2.58/1.17 % (2756665)Instructions burned: 182 (million)
% 2.58/1.17 % (2756667)Refutation found. Thanks to Tanya!
% 2.58/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.58/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.17 % (2756667)------------------------------
% 2.58/1.17 % (2756667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.17 % (2756667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.17 % (2756667)CaDiCaL version: 2.1.3
% 2.58/1.17 % (2756667)Termination reason: Refutation
% 2.58/1.17 % (2756667)Time elapsed: 0.022 s
% 2.58/1.17 % (2756667)Peak memory usage: 88 MB
% 2.58/1.17 % (2756667)Instructions burned: 71 (million)
% 2.58/1.17 % (2756667)------------------------------
% 2.58/1.17 % (2756667)------------------------------
% 2.58/1.17 % (2756582)Success in time 0.31 s
% 2.58/1.17 % Vampire exiting
%------------------------------------------------------------------------------