%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG128-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:35:38 PM UTC 2026
% Result : Unsatisfiable 2.35s 1.15s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of formulae : 87 ( 87 unt; 9 def)
% Number of atoms : 87 ( 86 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
fof(f2,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_001) ).
fof(f3,negated_conjecture,
! [X0,X1] : mult(X0,X1) = mult(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_002) ).
fof(f4,negated_conjecture,
! [X2,X0,X1] : mult(X0,add(X1,X2)) = add(mult(X0,X1),mult(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_003) ).
fof(f5,negated_conjecture,
! [X0] : add(zero,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_004) ).
fof(f6,negated_conjecture,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_005) ).
fof(f7,negated_conjecture,
! [X0] : add(unit,add(X0,mult(X0,X0))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_006) ).
fof(f8,negated_conjecture,
add(x0,x1) != mult(x0,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f9,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = mult(X0,add(X1,X2)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : mult(X0,add(X1,X2)) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = add(mult(X0,X1),mult(X0,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : add(mult(X0,X1),mult(X0,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X2,X0,X1] : sF0(X0,X1,X2) = sF1(X0,X1,X2),
inference(definition_folding,[],[f4,f12,f10]) ).
fof(f14,definition,
! [X0] : sF2(X0) = add(zero,X0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f15,plain,
! [X0] : add(zero,X0) = sF2(X0),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X0] : sF2(X0) = X0,
inference(definition_folding,[],[f5,f15]) ).
fof(f17,definition,
! [X0] : sF3(X0) = mult(X0,unit),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f18,plain,
! [X0] : mult(X0,unit) = sF3(X0),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0] : sF3(X0) = X0,
inference(definition_folding,[],[f6,f18]) ).
fof(f20,definition,
! [X0] : sF4(X0) = mult(X0,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f21,plain,
! [X0] : mult(X0,X0) = sF4(X0),
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
! [X0] : sF5(X0) = add(X0,sF4(X0)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f23,plain,
! [X0] : add(X0,sF4(X0)) = sF5(X0),
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
! [X0] : sF6(X0) = add(unit,sF5(X0)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f25,plain,
! [X0] : add(unit,sF5(X0)) = sF6(X0),
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
! [X0] : sF6(X0) = X0,
inference(definition_folding,[],[f7,f25,f23,f21]) ).
fof(f27,definition,
sF7 = add(x0,x1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f28,plain,
add(x0,x1) = sF7,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF8 = mult(x0,x1),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f30,plain,
mult(x0,x1) = sF8,
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
sF7 != sF8,
inference(definition_folding,[],[f8,f30,f28]) ).
fof(f32,plain,
! [X0] : add(unit,sF5(X0)) = X0,
inference(forward_demodulation,[],[f26,f25]) ).
fof(f33,plain,
! [X0] : mult(X0,unit) = X0,
inference(forward_demodulation,[],[f19,f18]) ).
fof(f34,plain,
! [X0] : add(zero,X0) = X0,
inference(forward_demodulation,[],[f16,f15]) ).
fof(f35,plain,
! [X2,X0,X1] : add(mult(X0,X1),mult(X0,X2)) = sF0(X0,X1,X2),
inference(forward_demodulation,[],[f13,f12]) ).
fof(f36,plain,
! [X0] : add(unit,add(X0,sF4(X0))) = X0,
inference(forward_demodulation,[],[f32,f23]) ).
fof(f37,plain,
! [X2,X0,X1] : mult(X0,add(X1,X2)) = add(mult(X0,X1),mult(X0,X2)),
inference(forward_demodulation,[],[f35,f10]) ).
fof(f38,plain,
! [X0] : add(unit,add(X0,mult(X0,X0))) = X0,
inference(forward_demodulation,[],[f36,f21]) ).
fof(f39,plain,
! [X0] : add(X0,zero) = X0,
inference(superposition,[],[f34,f2]) ).
fof(f59,plain,
unit = add(unit,add(unit,unit)),
inference(superposition,[],[f38,f33]) ).
fof(f62,plain,
zero = add(unit,mult(zero,zero)),
inference(superposition,[],[f38,f34]) ).
fof(f67,plain,
! [X0] : add(zero,X0) = add(unit,add(mult(zero,zero),X0)),
inference(superposition,[],[f1,f62]) ).
fof(f68,plain,
! [X0] : add(unit,add(mult(zero,zero),X0)) = X0,
inference(forward_demodulation,[],[f67,f34]) ).
fof(f75,plain,
! [X0] : mult(X0,unit) = add(mult(X0,unit),mult(X0,add(unit,unit))),
inference(superposition,[],[f37,f59]) ).
fof(f77,plain,
! [X0] : add(mult(X0,x0),mult(X0,x1)) = mult(X0,sF7),
inference(superposition,[],[f37,f28]) ).
fof(f89,plain,
! [X0] : mult(X0,unit) = add(mult(X0,unit),add(mult(X0,unit),mult(X0,unit))),
inference(forward_demodulation,[],[f75,f37]) ).
fof(f95,plain,
! [X0] : add(X0,add(X0,X0)) = X0,
inference(forward_demodulation,[],[f89,f33]) ).
fof(f118,plain,
! [X0] : add(unit,add(X0,mult(zero,zero))) = X0,
inference(superposition,[],[f68,f2]) ).
fof(f121,plain,
add(unit,mult(zero,zero)) = add(mult(zero,zero),mult(zero,zero)),
inference(superposition,[],[f68,f95]) ).
fof(f128,plain,
zero = add(mult(zero,zero),mult(zero,zero)),
inference(forward_demodulation,[],[f121,f62]) ).
fof(f141,plain,
mult(zero,zero) = add(unit,zero),
inference(superposition,[],[f118,f128]) ).
fof(f146,plain,
unit = mult(zero,zero),
inference(forward_demodulation,[],[f141,f39]) ).
fof(f148,plain,
zero = add(unit,unit),
inference(superposition,[],[f128,f146]) ).
fof(f156,plain,
! [X0] : mult(X0,zero) = add(mult(X0,unit),mult(X0,unit)),
inference(superposition,[],[f37,f148]) ).
fof(f159,plain,
! [X0] : mult(X0,zero) = add(X0,X0),
inference(forward_demodulation,[],[f156,f33]) ).
fof(f200,plain,
unit = add(zero,zero),
inference(superposition,[],[f146,f159]) ).
fof(f202,plain,
! [X0] : add(unit,add(X0,add(zero,zero))) = X0,
inference(superposition,[],[f118,f159]) ).
fof(f208,plain,
! [X0] : add(unit,add(X0,zero)) = X0,
inference(forward_demodulation,[],[f202,f39]) ).
fof(f210,plain,
zero = unit,
inference(forward_demodulation,[],[f200,f39]) ).
fof(f215,plain,
! [X0] : add(unit,X0) = X0,
inference(forward_demodulation,[],[f208,f39]) ).
fof(f228,plain,
! [X0] : mult(X0,unit) = add(X0,X0),
inference(superposition,[],[f159,f210]) ).
fof(f229,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f228,f33]) ).
fof(f236,plain,
! [X0] : add(X0,mult(X0,X0)) = X0,
inference(superposition,[],[f215,f38]) ).
fof(f256,plain,
! [X0,X1] : mult(X1,X0) = add(mult(X1,unit),mult(X1,X0)),
inference(superposition,[],[f37,f215]) ).
fof(f267,plain,
! [X0,X1] : mult(X1,X0) = add(X1,mult(X1,X0)),
inference(forward_demodulation,[],[f256,f33]) ).
fof(f416,plain,
sF8 = add(x0,sF8),
inference(superposition,[],[f267,f30]) ).
fof(f417,plain,
! [X0] : mult(X0,X0) = X0,
inference(superposition,[],[f267,f236]) ).
fof(f440,plain,
sF7 = add(mult(sF7,x0),mult(sF7,x1)),
inference(superposition,[],[f77,f417]) ).
fof(f448,plain,
sF7 = add(mult(sF7,x0),mult(x1,sF7)),
inference(forward_demodulation,[],[f440,f3]) ).
fof(f453,plain,
sF7 = add(mult(x1,sF7),mult(sF7,x0)),
inference(forward_demodulation,[],[f448,f2]) ).
fof(f457,plain,
sF7 = add(mult(x1,sF7),mult(x0,sF7)),
inference(forward_demodulation,[],[f453,f3]) ).
fof(f461,plain,
sF7 = add(mult(x0,sF7),mult(x1,sF7)),
inference(forward_demodulation,[],[f457,f2]) ).
fof(f465,plain,
sF7 = add(mult(x0,sF7),add(mult(x1,x0),mult(x1,x1))),
inference(forward_demodulation,[],[f461,f77]) ).
fof(f469,plain,
sF7 = add(mult(x0,sF7),add(mult(x1,x0),x1)),
inference(forward_demodulation,[],[f465,f417]) ).
fof(f473,plain,
sF7 = add(mult(x0,sF7),add(x1,mult(x1,x0))),
inference(forward_demodulation,[],[f469,f2]) ).
fof(f477,plain,
sF7 = add(mult(x0,sF7),mult(x1,x0)),
inference(forward_demodulation,[],[f473,f267]) ).
fof(f481,plain,
sF7 = add(mult(x0,sF7),mult(x0,x1)),
inference(forward_demodulation,[],[f477,f3]) ).
fof(f485,plain,
sF7 = add(mult(x0,x1),mult(x0,sF7)),
inference(forward_demodulation,[],[f481,f2]) ).
fof(f487,plain,
sF7 = add(mult(x0,x1),add(mult(x0,x0),mult(x0,x1))),
inference(forward_demodulation,[],[f485,f77]) ).
fof(f489,plain,
sF7 = add(sF8,add(mult(x0,x0),sF8)),
inference(forward_demodulation,[],[f487,f30]) ).
fof(f491,plain,
sF7 = add(sF8,add(sF8,mult(x0,x0))),
inference(forward_demodulation,[],[f489,f2]) ).
fof(f493,plain,
sF7 = add(sF8,add(sF8,x0)),
inference(forward_demodulation,[],[f491,f417]) ).
fof(f495,plain,
sF7 = add(sF8,add(x0,sF8)),
inference(forward_demodulation,[],[f493,f2]) ).
fof(f497,plain,
sF7 = add(sF8,sF8),
inference(forward_demodulation,[],[f495,f416]) ).
fof(f499,plain,
sF7 = sF8,
inference(forward_demodulation,[],[f497,f229]) ).
fof(f502,plain,
sF7 != sF7,
inference(superposition,[],[f31,f499]) ).
fof(f503,plain,
$false,
inference(trivial_inequality_removal,[],[f502]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG128-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.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 23:26:42 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 2.35/1.15 % (3324454)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.35/1.15 % (3324463)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3397384953:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.35/1.15 % (3324463)First to succeed.
% 2.35/1.15 % (3324463)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3324454"
% 2.35/1.15 % (3324465)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=312057547:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.35/1.15 % (3324460)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=3393794028:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.35/1.15 % (3324462)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2762151477:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.35/1.15 % (3324461)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=952818953:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.35/1.15 % (3324459)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=21550801:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.35/1.15 % (3324464)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1609615672:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.35/1.15 % (3324465)Also succeeded, but the first one will report.
% 2.35/1.15 % (3324462)Also succeeded, but the first one will report.
% 2.35/1.15 % (3324463)Refutation found. Thanks to Tanya!
% 2.35/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.35/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.34 % (3324463)------------------------------
% 2.63/1.34 % (3324463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.34 % (3324463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.34 % (3324463)CaDiCaL version: 2.1.3
% 2.63/1.34 % (3324463)Termination reason: Refutation
% 2.63/1.34 % (3324463)Time elapsed: 0.006 s
% 2.63/1.34 % (3324463)Peak memory usage: 88 MB
% 2.63/1.34 % (3324463)Instructions burned: 16 (million)
% 2.63/1.34 % (3324463)------------------------------
% 2.63/1.34 % (3324463)------------------------------
% 2.63/1.34 % (3324454)Success in time 0.287 s
% 2.63/1.34 % Vampire exiting
%------------------------------------------------------------------------------