%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 11:51:22 AM UTC 2026
% Result : Unsatisfiable 2.69s 1.35s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 64 ( 64 unt; 7 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : not(X0) = xor(X0,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,negated_conjecture,
! [X0] : xor(X0,falsehood) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,axiom,
! [X0] : xor(X0,X0) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f4,plain,
! [X0] : falsehood = xor(X0,X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : and_star(X0,truth) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f6,axiom,
! [X0] : and_star(X0,falsehood) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f7,plain,
! [X0] : falsehood = and_star(X0,falsehood),
inference(reorient_equations,[],[f6]) ).
fof(f10,axiom,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f11,axiom,
! [X0,X1] : and_star(xor(and_star(xor(truth,X0),X1),truth),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f12,axiom,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
fof(f14,axiom,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
fof(f15,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_definition) ).
fof(f16,plain,
falsehood = not(truth),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
! [X0,X1] : implies(X0,X1) = xor(truth,and_star(X0,xor(truth,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f18,negated_conjecture,
implies(truth,x) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
fof(f19,plain,
x != implies(truth,x),
inference(reorient_equations,[],[f18]) ).
fof(f20,plain,
falsehood = xor(truth,truth),
inference(definition_unfolding,[],[f16,f1]) ).
fof(f21,plain,
x != xor(truth,and_star(truth,xor(truth,x))),
inference(definition_unfolding,[],[f19,f17]) ).
fof(f22,definition,
! [X0] : sF0(X0) = xor(X0,falsehood),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
! [X0] : xor(X0,falsehood) = sF0(X0),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f2,f23]) ).
fof(f25,definition,
! [X0] : sF1(X0) = xor(X0,X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
! [X0] : xor(X0,X0) = sF1(X0),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : falsehood = sF1(X0),
inference(definition_folding,[],[f4,f26]) ).
fof(f28,definition,
! [X0] : sF2(X0) = and_star(X0,falsehood),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f29,plain,
! [X0] : and_star(X0,falsehood) = sF2(X0),
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
! [X0] : falsehood = sF2(X0),
inference(definition_folding,[],[f7,f29]) ).
fof(f36,definition,
sF5 = xor(truth,truth),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f37,plain,
xor(truth,truth) = sF5,
inference(reorient_equations,[],[f36]) ).
fof(f38,plain,
falsehood = sF5,
inference(definition_folding,[],[f20,f37]) ).
fof(f39,definition,
sF6 = xor(truth,x),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f40,plain,
xor(truth,x) = sF6,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF7 = and_star(truth,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f42,plain,
and_star(truth,sF6) = sF7,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF8 = xor(truth,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f44,plain,
xor(truth,sF7) = sF8,
inference(reorient_equations,[],[f43]) ).
fof(f45,plain,
x != sF8,
inference(definition_folding,[],[f21,f44,f42,f40]) ).
fof(f47,plain,
! [X0] : falsehood = and_star(X0,falsehood),
inference(forward_demodulation,[],[f30,f29]) ).
fof(f48,plain,
! [X0] : falsehood = xor(X0,X0),
inference(forward_demodulation,[],[f27,f26]) ).
fof(f49,plain,
! [X0] : xor(X0,falsehood) = X0,
inference(forward_demodulation,[],[f24,f23]) ).
fof(f52,plain,
! [X0] : falsehood = and_star(falsehood,X0),
inference(superposition,[],[f47,f14]) ).
fof(f84,plain,
! [X0] : falsehood = xor(X0,xor(truth,xor(X0,truth))),
inference(superposition,[],[f48,f10]) ).
fof(f85,plain,
! [X0] : xor(truth,xor(truth,X0)) = xor(falsehood,X0),
inference(superposition,[],[f10,f48]) ).
fof(f101,plain,
! [X0] : xor(falsehood,X0) = X0,
inference(superposition,[],[f49,f12]) ).
fof(f250,plain,
! [X0] : and_star(xor(and_star(falsehood,X0),truth),X0) = and_star(xor(and_star(xor(truth,X0),xor(truth,xor(truth,truth))),truth),xor(truth,xor(truth,truth))),
inference(superposition,[],[f11,f84]) ).
fof(f255,plain,
! [X0] : and_star(xor(and_star(falsehood,X0),truth),X0) = and_star(xor(truth,xor(truth,truth)),xor(and_star(xor(truth,X0),xor(truth,xor(truth,truth))),truth)),
inference(forward_demodulation,[],[f250,f14]) ).
fof(f265,plain,
! [X0] : and_star(xor(and_star(falsehood,X0),truth),X0) = and_star(xor(truth,xor(truth,truth)),xor(truth,and_star(xor(truth,X0),xor(truth,xor(truth,truth))))),
inference(forward_demodulation,[],[f255,f12]) ).
fof(f272,plain,
! [X0] : and_star(xor(and_star(falsehood,X0),truth),X0) = and_star(xor(truth,sF5),xor(truth,and_star(xor(truth,X0),xor(truth,sF5)))),
inference(forward_demodulation,[],[f265,f37]) ).
fof(f277,plain,
! [X0] : and_star(xor(and_star(falsehood,X0),truth),X0) = and_star(xor(truth,falsehood),xor(truth,and_star(xor(truth,X0),xor(truth,falsehood)))),
inference(forward_demodulation,[],[f272,f38]) ).
fof(f281,plain,
! [X0] : and_star(xor(and_star(falsehood,X0),truth),X0) = and_star(truth,xor(truth,and_star(xor(truth,X0),truth))),
inference(forward_demodulation,[],[f277,f49]) ).
fof(f283,plain,
! [X0] : and_star(xor(and_star(falsehood,X0),truth),X0) = and_star(truth,xor(truth,xor(truth,X0))),
inference(forward_demodulation,[],[f281,f5]) ).
fof(f285,plain,
! [X0] : and_star(X0,xor(and_star(falsehood,X0),truth)) = and_star(truth,xor(truth,xor(truth,X0))),
inference(forward_demodulation,[],[f283,f14]) ).
fof(f287,plain,
! [X0] : and_star(X0,xor(truth,and_star(falsehood,X0))) = and_star(truth,xor(truth,xor(truth,X0))),
inference(forward_demodulation,[],[f285,f12]) ).
fof(f289,plain,
! [X0] : and_star(truth,xor(truth,xor(truth,X0))) = and_star(X0,xor(truth,falsehood)),
inference(forward_demodulation,[],[f287,f52]) ).
fof(f291,plain,
! [X0] : and_star(X0,truth) = and_star(truth,xor(truth,xor(truth,X0))),
inference(forward_demodulation,[],[f289,f49]) ).
fof(f293,plain,
! [X0] : and_star(truth,xor(truth,xor(truth,X0))) = X0,
inference(forward_demodulation,[],[f291,f5]) ).
fof(f295,plain,
! [X0] : xor(truth,xor(truth,X0)) = X0,
inference(forward_demodulation,[],[f85,f101]) ).
fof(f297,plain,
x = xor(truth,sF6),
inference(superposition,[],[f295,f40]) ).
fof(f599,plain,
! [X0] : and_star(truth,X0) = X0,
inference(forward_demodulation,[],[f293,f295]) ).
fof(f600,plain,
sF6 = sF7,
inference(superposition,[],[f599,f42]) ).
fof(f636,plain,
sF8 = xor(truth,sF6),
inference(superposition,[],[f44,f600]) ).
fof(f645,plain,
x = sF8,
inference(forward_demodulation,[],[f636,f297]) ).
fof(f646,plain,
x != x,
inference(superposition,[],[f45,f645]) ).
fof(f656,plain,
$false,
inference(trivial_inequality_removal,[],[f646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 15:27:45 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.69/1.35 % (1781273)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.69/1.35 % (1781282)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2692659172:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.69/1.35 % (1781282)First to succeed.
% 2.69/1.35 % (1781282)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1781273"
% 2.69/1.35 % (1781281)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=656504033:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.69/1.35 % (1781279)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=3677372098:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.69/1.35 % (1781278)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=222373696:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.69/1.35 % (1781280)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1648136387:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.69/1.35 % (1781283)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2387900143:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.69/1.35 % (1781281)Also succeeded, but the first one will report.
% 2.69/1.35 % (1781284)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3158838501:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.69/1.35 % (1781284)Also succeeded, but the first one will report.
% 2.69/1.35 % (1781283)Also succeeded, but the first one will report.
% 2.69/1.35 % (1781282)Refutation found. Thanks to Tanya!
% 2.69/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.69/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.36 % (1781282)------------------------------
% 2.69/1.36 % (1781282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.36 % (1781282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.36 % (1781282)CaDiCaL version: 2.1.3
% 2.69/1.36 % (1781282)Termination reason: Refutation
% 2.69/1.36 % (1781282)Time elapsed: 0.007 s
% 2.69/1.36 % (1781282)Peak memory usage: 88 MB
% 2.69/1.36 % (1781282)Instructions burned: 21 (million)
% 2.69/1.36 % (1781282)------------------------------
% 2.69/1.36 % (1781282)------------------------------
% 2.69/1.36 % (1781273)Success in time 0.296 s
% 2.69/1.36 % Vampire exiting
%------------------------------------------------------------------------------