%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 11:58:41 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.47s
% Output : Refutation 0.12s
% 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f26,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(f27,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(f28,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,[],[f27,f1]) ).
fof(f29,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,[],[f26,f1]) ).
fof(f50,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,f29]) ).
fof(f55,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,[],[f50,f1]) ).
fof(f103,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,f28]) ).
fof(f107,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,[],[f103,f1]) ).
fof(f415,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,[],[f55,f23]) ).
fof(f423,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,[],[f415,f1]) ).
fof(f429,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,[],[f107,f423]) ).
fof(f442,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,[],[f429,f1]) ).
fof(f480,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,f442]) ).
fof(f490,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,[],[f480,f1]) ).
fof(f492,plain,
$false,
inference(forward_subsumption_resolution,[],[f490,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 15:41:26 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.47 % (1612456)Will run a generic schedule for satisfiability detection.
% 0.12/0.47 % (1612464)dis+10_1_sil=32000:sp=arity:random_seed=1974306420:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.47 % (1612462)% WARNING: option uhcvi not known.
% 0.12/0.47 % (1612461)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1563227299_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.47 % (1612466)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3439697753:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.47 % (1612467)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1345854485:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.47 % (1612463)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1863625908:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.47 % (1612465)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2306085373:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.47 % (1612462)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3616108774:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.47 % TRYING [1]
% 0.12/0.47 % (1612464) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1612456-1612464"...
% 0.12/0.47 % TRYING [2]
% 0.12/0.47 % (1612464)...printing done.
% 0.12/0.47 % (1612464)Refutation found. Thanks to Tanya!
% 0.12/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.47 % (1612464)------------------------------
% 0.12/0.47 % (1612464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.47 % (1612464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.47 % (1612464)CaDiCaL version: 2.1.3
% 0.12/0.47 % (1612464)Termination reason: Refutation
% 0.12/0.47 % (1612464)Time elapsed: 0.012 s
% 0.12/0.47 % (1612464)Peak memory usage: 11 MB
% 0.12/0.47 % (1612464)Instructions burned: 36 (million)
% 0.12/0.47 % (1612456)Success in time 0.037 s
% 0.12/0.47 % Vampire exiting
%------------------------------------------------------------------------------