%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL155-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 11:51:21 AM UTC 2026
% Result : Unsatisfiable 2.67s 1.28s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 24
% Syntax : Number of formulae : 90 ( 90 unt; 15 def)
% Number of atoms : 90 ( 89 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-2 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f4,negated_conjecture,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f6,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_definition) ).
fof(f9,axiom,
! [X0,X1] : or(X0,X1) = or(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
fof(f10,negated_conjecture,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition) ).
fof(f13,negated_conjecture,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).
fof(f19,negated_conjecture,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_definition) ).
fof(f20,negated_conjecture,
xor(x,x) != falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
fof(f21,plain,
falsehood != xor(x,x),
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
! [X0,X1] : and(X0,X1) = not(implies(not(not(X0)),not(X1))),
inference(definition_unfolding,[],[f10,f7]) ).
fof(f23,plain,
! [X0,X1] : xor(X0,X1) = implies(not(not(implies(not(not(X0)),not(not(X1))))),not(implies(not(not(not(X0))),not(X1)))),
inference(definition_unfolding,[],[f13,f7,f22,f22]) ).
fof(f26,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(definition_unfolding,[],[f9,f7,f7]) ).
fof(f32,plain,
falsehood != implies(not(not(implies(not(not(x)),not(not(x))))),not(implies(not(not(not(x))),not(x)))),
inference(definition_unfolding,[],[f21,f23]) ).
fof(f33,definition,
! [X0] : sF0(X0) = implies(truth,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f34,plain,
! [X0] : implies(truth,X0) = sF0(X0),
inference(reorient_equations,[],[f33]) ).
fof(f35,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f34]) ).
fof(f41,definition,
! [X0,X1] : sF3(X0,X1) = implies(implies(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f42,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = sF3(X0,X1),
inference(reorient_equations,[],[f41]) ).
fof(f43,plain,
! [X0,X1] : sF3(X0,X1) = sF3(X1,X0),
inference(definition_folding,[],[f4,f42,f42]) ).
fof(f44,definition,
! [X0,X1] : sF4(X0,X1) = implies(not(X0),not(X1)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f45,plain,
! [X0,X1] : implies(not(X0),not(X1)) = sF4(X0,X1),
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
! [X0,X1] : sF5(X0,X1) = implies(sF4(X0,X1),implies(X1,X0)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f47,plain,
! [X0,X1] : implies(sF4(X0,X1),implies(X1,X0)) = sF5(X0,X1),
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
! [X0,X1] : truth = sF5(X0,X1),
inference(definition_folding,[],[f6,f47,f45]) ).
fof(f49,definition,
! [X0,X1] : sF6(X0,X1) = implies(not(X0),X1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f50,plain,
! [X0,X1] : implies(not(X0),X1) = sF6(X0,X1),
inference(reorient_equations,[],[f49]) ).
fof(f58,plain,
! [X0,X1] : sF6(X0,X1) = sF6(X1,X0),
inference(definition_folding,[],[f26,f50,f50]) ).
fof(f96,definition,
sF26 = not(truth),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f97,plain,
not(truth) = sF26,
inference(reorient_equations,[],[f96]) ).
fof(f98,plain,
falsehood = sF26,
inference(definition_folding,[],[f19,f97]) ).
fof(f99,definition,
sF27 = not(x),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f100,plain,
not(x) = sF27,
inference(reorient_equations,[],[f99]) ).
fof(f101,definition,
sF28 = not(sF27),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f102,plain,
not(sF27) = sF28,
inference(reorient_equations,[],[f101]) ).
fof(f103,definition,
sF29 = implies(sF28,sF28),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f104,plain,
implies(sF28,sF28) = sF29,
inference(reorient_equations,[],[f103]) ).
fof(f105,definition,
sF30 = not(sF29),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f106,plain,
not(sF29) = sF30,
inference(reorient_equations,[],[f105]) ).
fof(f107,definition,
sF31 = not(sF30),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f108,plain,
not(sF30) = sF31,
inference(reorient_equations,[],[f107]) ).
fof(f109,definition,
sF32 = not(sF28),
introduced(definition,[new_symbols(definition,[sF32])],[function_definition]) ).
fof(f110,plain,
not(sF28) = sF32,
inference(reorient_equations,[],[f109]) ).
fof(f111,definition,
sF33 = implies(sF32,sF27),
introduced(definition,[new_symbols(definition,[sF33])],[function_definition]) ).
fof(f112,plain,
implies(sF32,sF27) = sF33,
inference(reorient_equations,[],[f111]) ).
fof(f113,definition,
sF34 = not(sF33),
introduced(definition,[new_symbols(definition,[sF34])],[function_definition]) ).
fof(f114,plain,
not(sF33) = sF34,
inference(reorient_equations,[],[f113]) ).
fof(f115,definition,
sF35 = implies(sF31,sF34),
introduced(definition,[new_symbols(definition,[sF35])],[function_definition]) ).
fof(f116,plain,
implies(sF31,sF34) = sF35,
inference(reorient_equations,[],[f115]) ).
fof(f117,plain,
falsehood != sF35,
inference(definition_folding,[],[f32,f116,f114,f112,f100,f110,f102,f100,f108,f106,f104,f102,f100,f102,f100]) ).
fof(f118,plain,
! [X0,X1] : implies(not(X1),X0) = sF6(X0,X1),
inference(forward_demodulation,[],[f58,f50]) ).
fof(f120,plain,
! [X0,X1] : truth = implies(sF4(X0,X1),implies(X1,X0)),
inference(forward_demodulation,[],[f48,f47]) ).
fof(f121,plain,
! [X0,X1] : implies(implies(X1,X0),X0) = sF3(X0,X1),
inference(forward_demodulation,[],[f43,f42]) ).
fof(f123,plain,
! [X0] : implies(truth,X0) = X0,
inference(forward_demodulation,[],[f35,f34]) ).
fof(f124,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(forward_demodulation,[],[f118,f50]) ).
fof(f126,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(forward_demodulation,[],[f120,f45]) ).
fof(f127,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(forward_demodulation,[],[f121,f42]) ).
fof(f137,plain,
! [X0] : implies(not(X0),sF27) = implies(sF28,X0),
inference(superposition,[],[f124,f102]) ).
fof(f138,plain,
! [X0] : implies(not(X0),sF28) = implies(sF32,X0),
inference(superposition,[],[f124,f110]) ).
fof(f140,plain,
! [X0] : implies(not(X0),sF30) = implies(sF31,X0),
inference(superposition,[],[f124,f108]) ).
fof(f217,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f126,f123]) ).
fof(f242,plain,
! [X0] : truth = implies(implies(not(X0),sF26),X0),
inference(forward_demodulation,[],[f217,f97]) ).
fof(f254,plain,
! [X0] : truth = implies(implies(not(X0),falsehood),X0),
inference(forward_demodulation,[],[f242,f98]) ).
fof(f289,plain,
implies(sF28,sF28) = implies(sF32,sF27),
inference(superposition,[],[f137,f110]) ).
fof(f299,plain,
implies(sF28,sF28) = sF33,
inference(forward_demodulation,[],[f289,f112]) ).
fof(f304,plain,
sF29 = sF33,
inference(forward_demodulation,[],[f299,f104]) ).
fof(f311,plain,
not(sF29) = sF34,
inference(superposition,[],[f114,f304]) ).
fof(f312,plain,
sF30 = sF34,
inference(forward_demodulation,[],[f311,f106]) ).
fof(f314,plain,
sF35 = implies(sF31,sF30),
inference(superposition,[],[f116,f312]) ).
fof(f363,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f127,f123]) ).
fof(f697,plain,
truth = implies(implies(sF32,falsehood),sF28),
inference(superposition,[],[f254,f110]) ).
fof(f701,plain,
! [X0] : truth = implies(implies(not(falsehood),X0),X0),
inference(superposition,[],[f254,f124]) ).
fof(f930,plain,
truth = implies(not(falsehood),not(falsehood)),
inference(superposition,[],[f363,f701]) ).
fof(f963,plain,
truth = implies(truth,not(falsehood)),
inference(superposition,[],[f701,f930]) ).
fof(f974,plain,
truth = not(falsehood),
inference(forward_demodulation,[],[f963,f123]) ).
fof(f985,plain,
implies(sF32,falsehood) = implies(truth,sF28),
inference(superposition,[],[f138,f974]) ).
fof(f987,plain,
implies(truth,sF30) = implies(sF31,falsehood),
inference(superposition,[],[f140,f974]) ).
fof(f992,plain,
sF30 = implies(sF31,falsehood),
inference(forward_demodulation,[],[f987,f123]) ).
fof(f994,plain,
sF28 = implies(sF32,falsehood),
inference(forward_demodulation,[],[f985,f123]) ).
fof(f1033,plain,
truth = implies(sF28,sF28),
inference(superposition,[],[f697,f994]) ).
fof(f1041,plain,
truth = sF29,
inference(forward_demodulation,[],[f1033,f104]) ).
fof(f1045,plain,
not(truth) = sF30,
inference(superposition,[],[f106,f1041]) ).
fof(f1058,plain,
sF26 = sF30,
inference(forward_demodulation,[],[f1045,f97]) ).
fof(f1060,plain,
falsehood = sF30,
inference(forward_demodulation,[],[f1058,f98]) ).
fof(f1065,plain,
sF35 = implies(sF31,falsehood),
inference(superposition,[],[f314,f1060]) ).
fof(f1075,plain,
sF30 = sF35,
inference(forward_demodulation,[],[f1065,f992]) ).
fof(f1079,plain,
falsehood = sF35,
inference(forward_demodulation,[],[f1075,f1060]) ).
fof(f1110,plain,
falsehood != falsehood,
inference(superposition,[],[f117,f1079]) ).
fof(f1111,plain,
$false,
inference(trivial_inequality_removal,[],[f1110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL155-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:24:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.67/1.28 % (4131591)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.67/1.28 % (4131601)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3088154070:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.67/1.28 % (4131600)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2097394825:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.67/1.28 % (4131598)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1528809069:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.67/1.28 % (4131596)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=2278321393:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.67/1.28 % (4131597)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=2875250819:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.67/1.28 % (4131599)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=380358065:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.67/1.28 % (4131602)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3071275602:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.67/1.28 % (4131600)First to succeed.
% 2.67/1.28 % (4131600)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4131591"
% 2.67/1.28 % (4131602)Also succeeded, but the first one will report.
% 2.67/1.28 % (4131599)Also succeeded, but the first one will report.
% 2.67/1.28 % (4131601)Instruction limit reached!
% 2.67/1.28 % (4131601)------------------------------
% 2.67/1.28 % (4131601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.28 % (4131601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.28 % (4131601)CaDiCaL version: 2.1.3
% 2.67/1.28 % (4131601)Termination reason: Instruction limit
% 2.67/1.28 % (4131601)Termination phase: Saturation
% 2.67/1.28 % (4131601)Time elapsed: 0.089 s
% 2.67/1.28 % (4131601)Peak memory usage: 90 MB
% 2.67/1.28 % (4131601)Instructions burned: 258 (million)
% 2.67/1.28 % (4131610)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=9820372:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 2.67/1.28 % (4131600)Refutation found. Thanks to Tanya!
% 2.67/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.67/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.48 % (4131600)------------------------------
% 3.54/1.48 % (4131600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.48 % (4131600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.48 % (4131600)CaDiCaL version: 2.1.3
% 3.54/1.48 % (4131600)Termination reason: Refutation
% 3.54/1.48 % (4131600)Time elapsed: 0.023 s
% 3.54/1.48 % (4131600)Peak memory usage: 89 MB
% 3.54/1.48 % (4131600)Instructions burned: 38 (million)
% 3.54/1.48 % (4131600)------------------------------
% 3.54/1.48 % (4131600)------------------------------
% 3.54/1.48 % (4131591)Success in time 0.424 s
% 3.54/1.48 % Vampire exiting
%------------------------------------------------------------------------------