%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL159-1 : 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 : 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 11:51:22 AM UTC 2026
% Result : Unsatisfiable 2.01s 1.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 97 ( 97 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f2,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
fof(f3,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [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,axiom,
! [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,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition) ).
fof(f11,axiom,
! [X2,X0,X1] : and(and(X0,X1),X2) = and(X0,and(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_associativity) ).
fof(f12,axiom,
! [X0,X1] : and(X0,X1) = and(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
fof(f13,axiom,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).
fof(f14,axiom,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
fof(f19,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_definition) ).
fof(f20,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
fof(f29,plain,
! [X0] : or(truth,X0) = implies(falsehood,X0),
inference(superposition,[],[f7,f19]) ).
fof(f30,plain,
! [X0] : implies(falsehood,X0) = or(X0,truth),
inference(superposition,[],[f29,f9]) ).
fof(f38,plain,
! [X0] : and(truth,X0) = not(or(falsehood,not(X0))),
inference(superposition,[],[f10,f19]) ).
fof(f40,plain,
! [X0] : and(X0,truth) = not(or(not(X0),falsehood)),
inference(superposition,[],[f10,f19]) ).
fof(f42,plain,
! [X0,X1] : not(or(not(X0),not(X1))) = and(X1,X0),
inference(superposition,[],[f10,f9]) ).
fof(f45,plain,
! [X0] : not(or(falsehood,not(X0))) = and(X0,truth),
inference(forward_demodulation,[],[f40,f9]) ).
fof(f46,plain,
and(truth,truth) = not(or(falsehood,falsehood)),
inference(superposition,[],[f38,f19]) ).
fof(f82,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f97,plain,
! [X0] : implies(implies(not(X0),truth),truth) = or(X0,not(X0)),
inference(superposition,[],[f7,f82]) ).
fof(f98,plain,
! [X0] : implies(or(X0,truth),truth) = or(X0,not(X0)),
inference(forward_demodulation,[],[f97,f7]) ).
fof(f103,plain,
! [X0] : or(X0,not(X0)) = implies(implies(falsehood,X0),truth),
inference(forward_demodulation,[],[f98,f30]) ).
fof(f158,plain,
! [X0,X1] : truth = implies(or(X0,not(X1)),implies(X1,X0)),
inference(forward_demodulation,[],[f6,f7]) ).
fof(f166,plain,
! [X0,X1] : truth = implies(or(not(X0),X1),implies(X0,X1)),
inference(superposition,[],[f158,f9]) ).
fof(f170,plain,
! [X0] : truth = implies(or(X0,not(truth)),X0),
inference(superposition,[],[f158,f1]) ).
fof(f179,plain,
! [X0] : truth = implies(or(X0,falsehood),X0),
inference(forward_demodulation,[],[f170,f19]) ).
fof(f181,plain,
! [X0] : truth = implies(or(falsehood,X0),X0),
inference(superposition,[],[f179,f9]) ).
fof(f183,plain,
truth = implies(implies(falsehood,falsehood),truth),
inference(superposition,[],[f179,f29]) ).
fof(f187,plain,
truth = or(falsehood,not(falsehood)),
inference(forward_demodulation,[],[f183,f103]) ).
fof(f224,plain,
truth = implies(truth,not(falsehood)),
inference(superposition,[],[f181,f187]) ).
fof(f232,plain,
truth = not(falsehood),
inference(forward_demodulation,[],[f224,f1]) ).
fof(f235,plain,
! [X0] : implies(truth,X0) = or(falsehood,X0),
inference(superposition,[],[f7,f232]) ).
fof(f239,plain,
! [X0] : not(or(truth,not(X0))) = and(X0,falsehood),
inference(superposition,[],[f42,f232]) ).
fof(f246,plain,
! [X0] : and(X0,falsehood) = not(implies(falsehood,not(X0))),
inference(forward_demodulation,[],[f239,f29]) ).
fof(f250,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[],[f235,f1]) ).
fof(f263,plain,
! [X0] : or(X0,falsehood) = X0,
inference(superposition,[],[f250,f9]) ).
fof(f266,plain,
! [X0] : and(X0,truth) = not(not(X0)),
inference(superposition,[],[f45,f250]) ).
fof(f267,plain,
! [X0] : and(truth,X0) = not(not(X0)),
inference(superposition,[],[f38,f250]) ).
fof(f270,plain,
! [X0] : truth = implies(X0,X0),
inference(superposition,[],[f181,f250]) ).
fof(f293,plain,
! [X0] : truth = or(X0,not(X0)),
inference(superposition,[],[f270,f7]) ).
fof(f318,plain,
! [X0] : truth = implies(implies(falsehood,X0),truth),
inference(superposition,[],[f293,f103]) ).
fof(f508,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f537,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f508,f1]) ).
fof(f617,plain,
! [X0,X1] : xor(or(falsehood,not(X0)),X1) = or(and(or(falsehood,not(X0)),not(X1)),and(and(X0,truth),X1)),
inference(superposition,[],[f13,f45]) ).
fof(f631,plain,
! [X0,X1] : xor(or(falsehood,not(X0)),X1) = or(and(and(X0,truth),X1),and(or(falsehood,not(X0)),not(X1))),
inference(forward_demodulation,[],[f617,f9]) ).
fof(f647,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(and(X0,truth),X1),and(not(X0),not(X1))),
inference(forward_demodulation,[],[f631,f250]) ).
fof(f661,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(not(X0),not(X1)),and(and(X0,truth),X1)),
inference(forward_demodulation,[],[f647,f9]) ).
fof(f666,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(not(X0),not(X1)),and(X0,and(truth,X1))),
inference(forward_demodulation,[],[f661,f11]) ).
fof(f670,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(X0,and(truth,X1)),and(not(X0),not(X1))),
inference(forward_demodulation,[],[f666,f9]) ).
fof(f674,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(X0,not(not(X1))),and(not(X0),not(X1))),
inference(forward_demodulation,[],[f670,f267]) ).
fof(f675,plain,
! [X0,X1] : xor(not(X0),X1) = xor(X0,not(X1)),
inference(forward_demodulation,[],[f674,f13]) ).
fof(f767,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f537,f82]) ).
fof(f792,plain,
! [X0] : truth = implies(X0,truth),
inference(forward_demodulation,[],[f767,f270]) ).
fof(f814,plain,
! [X0] : truth = or(X0,truth),
inference(superposition,[],[f792,f7]) ).
fof(f849,plain,
! [X0] : truth = implies(falsehood,X0),
inference(superposition,[],[f814,f30]) ).
fof(f951,plain,
! [X0] : truth = implies(implies(implies(falsehood,not(X0)),truth),implies(X0,not(not(X0)))),
inference(superposition,[],[f166,f103]) ).
fof(f990,plain,
! [X0] : truth = implies(truth,implies(X0,not(not(X0)))),
inference(forward_demodulation,[],[f951,f318]) ).
fof(f999,plain,
! [X0] : truth = implies(X0,not(not(X0))),
inference(forward_demodulation,[],[f990,f1]) ).
fof(f1020,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(superposition,[],[f4,f999]) ).
fof(f1030,plain,
! [X0] : not(not(X0)) = implies(implies(not(not(X0)),X0),X0),
inference(forward_demodulation,[],[f1020,f1]) ).
fof(f1040,plain,
! [X0] : not(not(X0)) = implies(or(not(X0),X0),X0),
inference(forward_demodulation,[],[f1030,f7]) ).
fof(f1046,plain,
! [X0] : not(not(X0)) = implies(or(X0,not(X0)),X0),
inference(forward_demodulation,[],[f1040,f9]) ).
fof(f1049,plain,
! [X0] : implies(truth,X0) = not(not(X0)),
inference(forward_demodulation,[],[f1046,f293]) ).
fof(f1052,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[],[f1049,f1]) ).
fof(f1904,plain,
! [X0] : xor(or(falsehood,falsehood),not(X0)) = xor(and(truth,truth),X0),
inference(superposition,[],[f675,f46]) ).
fof(f1906,plain,
! [X0,X1] : xor(X1,not(X0)) = xor(X0,not(X1)),
inference(superposition,[],[f675,f14]) ).
fof(f1916,plain,
! [X0] : xor(or(falsehood,falsehood),not(X0)) = xor(not(not(truth)),X0),
inference(forward_demodulation,[],[f1904,f266]) ).
fof(f1922,plain,
! [X0] : xor(or(falsehood,falsehood),not(X0)) = xor(not(truth),not(X0)),
inference(forward_demodulation,[],[f1916,f675]) ).
fof(f1925,plain,
! [X0] : xor(or(falsehood,falsehood),not(X0)) = xor(truth,not(not(X0))),
inference(forward_demodulation,[],[f1922,f675]) ).
fof(f1928,plain,
! [X0] : xor(truth,X0) = xor(or(falsehood,falsehood),not(X0)),
inference(forward_demodulation,[],[f1925,f1052]) ).
fof(f1929,plain,
! [X0] : xor(truth,X0) = xor(falsehood,not(X0)),
inference(forward_demodulation,[],[f1928,f263]) ).
fof(f2553,plain,
! [X0] : not(truth) = and(X0,falsehood),
inference(forward_demodulation,[],[f246,f849]) ).
fof(f2554,plain,
! [X0] : falsehood = and(X0,falsehood),
inference(forward_demodulation,[],[f2553,f19]) ).
fof(f2555,plain,
! [X0] : falsehood = and(falsehood,X0),
inference(superposition,[],[f2554,f12]) ).
fof(f2563,plain,
! [X0] : xor(X0,falsehood) = or(and(X0,not(falsehood)),falsehood),
inference(superposition,[],[f13,f2554]) ).
fof(f2566,plain,
! [X0] : xor(X0,falsehood) = or(falsehood,and(X0,not(falsehood))),
inference(forward_demodulation,[],[f2563,f9]) ).
fof(f2568,plain,
! [X0] : xor(X0,falsehood) = and(X0,not(falsehood)),
inference(forward_demodulation,[],[f2566,f250]) ).
fof(f2569,plain,
! [X0] : and(X0,truth) = xor(X0,falsehood),
inference(forward_demodulation,[],[f2568,f232]) ).
fof(f2570,plain,
! [X0] : not(not(X0)) = xor(X0,falsehood),
inference(forward_demodulation,[],[f2569,f266]) ).
fof(f2571,plain,
! [X0] : xor(X0,falsehood) = X0,
inference(forward_demodulation,[],[f2570,f1052]) ).
fof(f2579,plain,
! [X0] : xor(falsehood,X0) = or(falsehood,and(not(falsehood),X0)),
inference(superposition,[],[f13,f2555]) ).
fof(f2580,plain,
! [X0] : xor(falsehood,X0) = and(not(falsehood),X0),
inference(forward_demodulation,[],[f2579,f250]) ).
fof(f2582,plain,
! [X0] : and(truth,X0) = xor(falsehood,X0),
inference(forward_demodulation,[],[f2580,f232]) ).
fof(f2583,plain,
! [X0] : not(not(X0)) = xor(falsehood,X0),
inference(forward_demodulation,[],[f2582,f267]) ).
fof(f2584,plain,
! [X0] : xor(falsehood,X0) = X0,
inference(forward_demodulation,[],[f2583,f1052]) ).
fof(f2590,plain,
! [X0] : not(X0) = xor(X0,not(falsehood)),
inference(superposition,[],[f675,f2571]) ).
fof(f2591,plain,
! [X0] : not(X0) = xor(X0,truth),
inference(forward_demodulation,[],[f2590,f232]) ).
fof(f2594,plain,
! [X0] : not(X0) = xor(truth,X0),
inference(superposition,[],[f2584,f1929]) ).
fof(f2679,plain,
xor(x,xor(truth,y)) != xor(not(x),y),
inference(superposition,[],[f20,f2591]) ).
fof(f2680,plain,
xor(x,xor(truth,y)) != xor(y,not(x)),
inference(forward_demodulation,[],[f2679,f14]) ).
fof(f2683,plain,
xor(x,xor(truth,y)) != xor(x,not(y)),
inference(forward_demodulation,[],[f2680,f1906]) ).
fof(f2698,plain,
xor(x,not(y)) != xor(x,not(y)),
inference(superposition,[],[f2683,f2594]) ).
fof(f2706,plain,
$false,
inference(trivial_inequality_removal,[],[f2698]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n007.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 15:22:25 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.01/1.30 % (1581713)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.01/1.30 % (1581720)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=442008890:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.01/1.30 % (1581718)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=1926190442:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.01/1.30 % (1581723)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1984127117:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.01/1.30 % (1581721)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1022058079:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.01/1.30 % (1581724)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=49123028:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.01/1.30 % (1581722)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2967252914:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.01/1.30 % (1581719)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=1291184:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.01/1.30 % (1581724)First to succeed.
% 2.01/1.30 % (1581724)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1581713"
% 2.01/1.30 % (1581721)Also succeeded, but the first one will report.
% 2.01/1.30 % (1581722)Instruction limit reached!
% 2.01/1.30 % (1581722)------------------------------
% 2.01/1.30 % (1581722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/1.30 % (1581722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/1.30 % (1581722)CaDiCaL version: 2.1.3
% 2.01/1.30 % (1581722)Termination reason: Instruction limit
% 2.01/1.30 % (1581722)Termination phase: Saturation
% 2.01/1.30 % (1581722)Time elapsed: 0.097 s
% 2.01/1.30 % (1581722)Peak memory usage: 90 MB
% 2.01/1.30 % (1581722)Instructions burned: 182 (million)
% 2.01/1.30 % (1581723)Instruction limit reached!
% 2.01/1.30 % (1581723)------------------------------
% 2.01/1.30 % (1581723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/1.30 % (1581723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/1.30 % (1581723)CaDiCaL version: 2.1.3
% 2.01/1.30 % (1581723)Termination reason: Instruction limit
% 2.01/1.30 % (1581723)Termination phase: Saturation
% 2.01/1.30 % (1581723)Time elapsed: 0.166 s
% 2.01/1.30 % (1581723)Peak memory usage: 90 MB
% 2.01/1.30 % (1581723)Instructions burned: 258 (million)
% 2.01/1.30 % (1581732)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3794748943:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 2.01/1.30 % (1581724)Refutation found. Thanks to Tanya!
% 2.01/1.30 % SZS status Unsatisfiable for theBenchmark
% 2.01/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.50 % (1581724)------------------------------
% 0.18/1.50 % (1581724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (1581724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (1581724)CaDiCaL version: 2.1.3
% 0.18/1.50 % (1581724)Termination reason: Refutation
% 0.18/1.50 % (1581724)Time elapsed: 0.044 s
% 0.18/1.50 % (1581724)Peak memory usage: 88 MB
% 0.18/1.50 % (1581724)Instructions burned: 75 (million)
% 0.18/1.50 % (1581724)------------------------------
% 0.18/1.50 % (1581724)------------------------------
% 0.18/1.50 % (1581713)Success in time 0.449 s
% 0.18/1.50 % Vampire exiting
%------------------------------------------------------------------------------