%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:35:56 AM UTC 2026
% Result : Unsatisfiable 5.24s 1.64s
% Output : Refutation 6.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 6
% Syntax : Number of formulae : 72 ( 72 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 100 ( 100 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
fof(f3,axiom,
! [X0] : add(X0,inverse(X0)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
fof(f4,axiom,
! [X2,X0,X1] : pixley(X0,X1,X2) = add(multiply(X0,inverse(X1)),add(multiply(X0,X2),multiply(inverse(X1),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley_defn) ).
fof(f5,axiom,
! [X0,X1] : pixley(X0,X0,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley1) ).
fof(f8,negated_conjecture,
add(multiply(a,b),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_add_multiply) ).
fof(f9,plain,
b != add(multiply(a,b),b),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X0] : inverse(X0) = multiply(n1,inverse(X0)),
inference(superposition,[],[f1,f3]) ).
fof(f11,plain,
! [X2,X0,X1] : multiply(X0,add(add(X1,X0),X2)) = add(X0,multiply(X2,X0)),
inference(superposition,[],[f2,f1]) ).
fof(f12,plain,
! [X0,X1] : multiply(inverse(X0),add(n1,X1)) = add(inverse(X0),multiply(X1,inverse(X0))),
inference(superposition,[],[f2,f10]) ).
fof(f13,plain,
! [X2,X0,X1] : multiply(X0,add(X1,add(X2,X0))) = add(multiply(X1,X0),X0),
inference(superposition,[],[f2,f1]) ).
fof(f15,plain,
! [X2,X0,X1] : multiply(X2,X0) = multiply(multiply(X0,add(X1,X2)),multiply(X2,X0)),
inference(superposition,[],[f1,f2]) ).
fof(f18,plain,
! [X0,X1] : add(X0,multiply(inverse(add(X1,X0)),X0)) = multiply(X0,n1),
inference(superposition,[],[f11,f3]) ).
fof(f21,plain,
! [X2,X0,X1] : pixley(X0,X1,X2) = add(multiply(X0,inverse(X1)),multiply(X2,add(X0,inverse(X1)))),
inference(forward_demodulation,[],[f4,f2]) ).
fof(f30,plain,
! [X2,X3,X0,X1] : add(multiply(X3,multiply(X2,X0)),multiply(X2,X0)) = multiply(multiply(X2,X0),add(X3,multiply(X0,add(X1,X2)))),
inference(superposition,[],[f13,f2]) ).
fof(f37,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(multiply(X1,n1),multiply(inverse(X0),X1)),
inference(superposition,[],[f15,f3]) ).
fof(f71,plain,
! [X0] : add(inverse(X0),inverse(X0)) = multiply(inverse(X0),add(n1,n1)),
inference(superposition,[],[f12,f10]) ).
fof(f85,plain,
! [X0,X1] : pixley(X0,X0,X1) = add(multiply(X0,inverse(X0)),multiply(X1,n1)),
inference(superposition,[],[f21,f3]) ).
fof(f93,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),multiply(X1,n1)) = X1,
inference(forward_demodulation,[],[f85,f5]) ).
fof(f94,plain,
! [X0] : add(inverse(n1),multiply(X0,n1)) = X0,
inference(superposition,[],[f93,f10]) ).
fof(f97,plain,
! [X0,X1] : add(multiply(X1,multiply(X0,n1)),multiply(X0,n1)) = multiply(multiply(X0,n1),add(X1,X0)),
inference(superposition,[],[f13,f93]) ).
fof(f99,plain,
! [X2,X0] : add(multiply(X0,n1),multiply(X2,multiply(X0,n1))) = multiply(multiply(X0,n1),add(X0,X2)),
inference(superposition,[],[f11,f93]) ).
fof(f100,plain,
! [X0] : multiply(X0,n1) = multiply(X0,multiply(X0,n1)),
inference(superposition,[],[f1,f93]) ).
fof(f101,plain,
! [X0] : add(X0,n1) = add(inverse(n1),n1),
inference(superposition,[],[f94,f1]) ).
fof(f107,plain,
! [X0,X1] : add(X1,n1) = add(X0,n1),
inference(superposition,[],[f101,f101]) ).
fof(f136,plain,
! [X0,X1] : multiply(X1,add(X0,n1)) = add(X1,multiply(n1,X1)),
inference(superposition,[],[f11,f107]) ).
fof(f172,plain,
! [X2,X0,X1] : multiply(X0,add(X1,n1)) = multiply(X0,add(X2,n1)),
inference(superposition,[],[f136,f136]) ).
fof(f200,plain,
! [X2,X0,X1] : add(X0,n1) = multiply(add(X1,add(X0,n1)),add(X2,n1)),
inference(superposition,[],[f172,f1]) ).
fof(f236,plain,
! [X0,X1] : multiply(inverse(X1),add(X0,n1)) = add(inverse(X1),inverse(X1)),
inference(superposition,[],[f71,f107]) ).
fof(f248,plain,
! [X0] : add(inverse(X0),inverse(X0)) = multiply(multiply(add(n1,n1),n1),add(inverse(X0),inverse(X0))),
inference(superposition,[],[f37,f71]) ).
fof(f256,plain,
! [X0] : add(inverse(X0),inverse(X0)) = multiply(n1,add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[],[f248,f1]) ).
fof(f363,plain,
! [X0,X1] : multiply(n1,add(X1,add(X0,n1))) = multiply(add(X0,n1),multiply(n1,add(X1,add(X0,n1)))),
inference(superposition,[],[f15,f200]) ).
fof(f367,plain,
! [X0,X1] : add(multiply(X1,n1),n1) = multiply(add(X0,n1),add(multiply(X1,n1),n1)),
inference(forward_demodulation,[],[f363,f13]) ).
fof(f372,plain,
! [X0] : add(inverse(n1),n1) = multiply(add(X0,n1),add(inverse(n1),n1)),
inference(forward_demodulation,[],[f367,f101]) ).
fof(f396,plain,
! [X0,X1] : add(X0,n1) = multiply(add(X1,n1),add(X0,n1)),
inference(superposition,[],[f372,f101]) ).
fof(f1623,plain,
! [X0] : add(multiply(X0,n1),multiply(X0,n1)) = multiply(multiply(X0,n1),add(X0,X0)),
inference(superposition,[],[f97,f100]) ).
fof(f1650,plain,
! [X0] : multiply(n1,add(X0,X0)) = multiply(multiply(X0,n1),add(X0,X0)),
inference(forward_demodulation,[],[f1623,f2]) ).
fof(f1653,plain,
! [X0] : multiply(n1,add(X0,n1)) = multiply(multiply(n1,n1),add(X0,n1)),
inference(superposition,[],[f1650,f107]) ).
fof(f1702,plain,
! [X0,X1] : multiply(add(X0,n1),add(X1,multiply(n1,n1))) = add(multiply(X1,add(X0,n1)),multiply(n1,add(X0,n1))),
inference(superposition,[],[f2,f1653]) ).
fof(f1705,plain,
! [X0,X1] : multiply(add(X0,n1),add(X1,n1)) = multiply(add(X0,n1),add(X1,multiply(n1,n1))),
inference(forward_demodulation,[],[f1702,f2]) ).
fof(f1719,plain,
! [X0,X1] : add(X1,n1) = multiply(add(X0,n1),add(X1,multiply(n1,n1))),
inference(forward_demodulation,[],[f1705,f396]) ).
fof(f1744,plain,
! [X0] : multiply(add(X0,n1),n1) = add(inverse(n1),n1),
inference(superposition,[],[f1719,f94]) ).
fof(f1756,plain,
n1 = add(inverse(n1),n1),
inference(forward_demodulation,[],[f1744,f1]) ).
fof(f1773,plain,
! [X0] : multiply(X0,n1) = add(X0,multiply(n1,X0)),
inference(superposition,[],[f136,f1756]) ).
fof(f1779,plain,
! [X0] : multiply(inverse(X0),n1) = add(inverse(X0),inverse(X0)),
inference(superposition,[],[f236,f1756]) ).
fof(f1808,plain,
n1 = multiply(n1,n1),
inference(superposition,[],[f1,f1756]) ).
fof(f1812,plain,
multiply(n1,n1) = add(n1,multiply(inverse(n1),n1)),
inference(superposition,[],[f18,f1756]) ).
fof(f3849,plain,
n1 = add(n1,multiply(inverse(n1),n1)),
inference(forward_demodulation,[],[f1812,f1808]) ).
fof(f3857,plain,
multiply(multiply(inverse(n1),n1),n1) = add(multiply(inverse(n1),n1),multiply(inverse(n1),multiply(inverse(n1),n1))),
inference(superposition,[],[f18,f3849]) ).
fof(f3869,plain,
multiply(multiply(inverse(n1),n1),n1) = multiply(multiply(inverse(n1),n1),add(inverse(n1),inverse(n1))),
inference(forward_demodulation,[],[f3857,f99]) ).
fof(f3876,plain,
multiply(n1,add(inverse(n1),inverse(n1))) = multiply(multiply(inverse(n1),n1),n1),
inference(forward_demodulation,[],[f3869,f1650]) ).
fof(f3879,plain,
add(inverse(n1),inverse(n1)) = multiply(multiply(inverse(n1),n1),n1),
inference(forward_demodulation,[],[f3876,f256]) ).
fof(f3880,plain,
multiply(inverse(n1),n1) = multiply(multiply(inverse(n1),n1),n1),
inference(forward_demodulation,[],[f3879,f1779]) ).
fof(f6704,plain,
multiply(inverse(n1),n1) = add(inverse(n1),multiply(inverse(n1),n1)),
inference(superposition,[],[f94,f3880]) ).
fof(f6742,plain,
inverse(n1) = multiply(inverse(n1),n1),
inference(forward_demodulation,[],[f6704,f94]) ).
fof(f6779,plain,
! [X0] : add(inverse(n1),multiply(X0,n1)) = multiply(n1,add(inverse(n1),X0)),
inference(superposition,[],[f2,f6742]) ).
fof(f6801,plain,
! [X0] : multiply(n1,add(inverse(n1),X0)) = X0,
inference(forward_demodulation,[],[f6779,f94]) ).
fof(f7323,plain,
! [X0] : multiply(X0,n1) = multiply(n1,X0),
inference(superposition,[],[f6801,f94]) ).
fof(f7543,plain,
! [X0] : multiply(X0,n1) = add(X0,multiply(X0,n1)),
inference(superposition,[],[f1773,f7323]) ).
fof(f8322,plain,
! [X0] : multiply(n1,X0) = add(X0,multiply(n1,X0)),
inference(superposition,[],[f7543,f7323]) ).
fof(f9545,plain,
! [X0] : add(add(inverse(n1),X0),X0) = X0,
inference(superposition,[],[f8322,f6801]) ).
fof(f9734,plain,
! [X0] : multiply(X0,X0) = add(X0,multiply(X0,X0)),
inference(superposition,[],[f11,f9545]) ).
fof(f9736,plain,
! [X0] : multiply(X0,X0) = X0,
inference(superposition,[],[f1,f9545]) ).
fof(f10255,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f9734,f9736]) ).
fof(f10350,plain,
! [X0,X1] : add(X1,multiply(add(X0,X1),X1)) = multiply(X1,add(X0,X1)),
inference(superposition,[],[f11,f10255]) ).
fof(f10369,plain,
! [X0,X1] : add(X1,X1) = multiply(X1,add(X0,X1)),
inference(forward_demodulation,[],[f10350,f1]) ).
fof(f10424,plain,
! [X0,X1] : multiply(X1,add(X0,X1)) = X1,
inference(forward_demodulation,[],[f10369,f10255]) ).
fof(f11153,plain,
! [X0,X1] : add(multiply(X1,multiply(X0,X0)),multiply(X0,X0)) = multiply(multiply(X0,X0),add(X1,X0)),
inference(superposition,[],[f30,f10424]) ).
fof(f11247,plain,
! [X0,X1] : add(multiply(X1,X0),X0) = multiply(X0,add(X1,X0)),
inference(forward_demodulation,[],[f11153,f9736]) ).
fof(f11284,plain,
! [X0,X1] : add(multiply(X1,X0),X0) = X0,
inference(forward_demodulation,[],[f11247,f10424]) ).
fof(f11408,plain,
b != b,
inference(superposition,[],[f9,f11284]) ).
fof(f11499,plain,
$false,
inference(trivial_inequality_removal,[],[f11408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n020.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 21:05:19 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 Running first-order theorem proving
% 0.10/0.27 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
% 5.24/1.64 % (558533)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.24/1.64 % (558539)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=1229568383:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.24/1.64 % (558540)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2558224001:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.24/1.64 % (558538)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=1615685283:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.24/1.64 % (558541)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2259353818:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.24/1.64 % (558542)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3911014166:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.24/1.64 % (558544)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1808263611:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.24/1.64 % (558543)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3264249896:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.24/1.64 % (558541)Instruction limit reached!
% 5.24/1.64 % (558541)------------------------------
% 5.24/1.64 % (558541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.64 % (558541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.64 % (558541)CaDiCaL version: 2.1.3
% 5.24/1.64 % (558541)Termination reason: Instruction limit
% 5.24/1.64 % (558541)Termination phase: Saturation
% 5.24/1.64 % (558541)Time elapsed: 0.133 s
% 5.24/1.64 % (558541)Peak memory usage: 89 MB
% 5.24/1.64 % (558541)Instructions burned: 136 (million)
% 5.24/1.64 % (558542)Instruction limit reached!
% 5.24/1.64 % (558542)------------------------------
% 5.24/1.64 % (558542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.64 % (558542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.64 % (558542)CaDiCaL version: 2.1.3
% 5.24/1.64 % (558542)Termination reason: Instruction limit
% 5.24/1.64 % (558542)Termination phase: Saturation
% 5.24/1.64 % (558542)Time elapsed: 0.169 s
% 5.24/1.64 % (558542)Peak memory usage: 89 MB
% 5.24/1.64 % (558542)Instructions burned: 181 (million)
% 5.24/1.64 % (558543)Instruction limit reached!
% 5.24/1.64 % (558543)------------------------------
% 5.24/1.64 % (558543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/1.64 % (558543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/1.64 % (558543)CaDiCaL version: 2.1.3
% 5.24/1.64 % (558543)Termination reason: Instruction limit
% 5.24/1.64 % (558543)Termination phase: Saturation
% 5.24/1.64 % (558543)Time elapsed: 0.286 s
% 5.24/1.64 % (558543)Peak memory usage: 91 MB
% 5.24/1.64 % (558543)Instructions burned: 257 (million)
% 5.24/1.64 % (558544)First to succeed.
% 5.24/1.64 % (558544)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-558533"
% 5.24/1.64 % (558552)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1004804450:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 5.24/1.64 % (558553)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1944589125:i=4948:ss=axioms:sgt=16_2994 on theBenchmark for (2994ds/4948Mi)
% 5.24/1.64 % (558554)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2906237350:i=215:ep=RSTC_2993 on theBenchmark for (2993ds/215Mi)
% 5.24/1.64 % (558544)Refutation found. Thanks to Tanya!
% 5.24/1.64 % SZS status Unsatisfiable for theBenchmark
% 5.24/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 6.57/1.78 % (558544)------------------------------
% 6.57/1.78 % (558544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.78 % (558544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.78 % (558544)CaDiCaL version: 2.1.3
% 6.57/1.78 % (558544)Termination reason: Refutation
% 6.57/1.78 % (558544)Time elapsed: 0.310 s
% 6.57/1.78 % (558544)Peak memory usage: 91 MB
% 6.57/1.78 % (558544)Instructions burned: 391 (million)
% 6.57/1.78 % (558544)------------------------------
% 6.57/1.78 % (558544)------------------------------
% 6.57/1.78 % (558533)Success in time 0.9 s
% 6.57/1.78 % Vampire exiting
%------------------------------------------------------------------------------