%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 09:35:55 AM UTC 2026
% Result : Unsatisfiable 8.38s 1.78s
% Output : Refutation 8.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
fof(f3,axiom,
! [X0] : add(X0,inverse(X0)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
fof(f4,axiom,
! [X0,X1] : add(multiply(X0,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply) ).
fof(f5,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X1,X0),add(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
fof(f6,axiom,
! [X0] : multiply(X0,inverse(X0)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).
fof(f7,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
fof(f13,plain,
! [X0,X1] : add(inverse(X0),multiply(X1,X0)) = multiply(add(X1,inverse(X0)),n1),
inference(superposition,[],[f5,f3]) ).
fof(f19,plain,
! [X1] : multiply(X1,X1) = X1,
inference(superposition,[],[f1,f4]) ).
fof(f27,plain,
! [X0,X1] : add(multiply(X1,X0),X0) = multiply(X0,add(X1,X0)),
inference(superposition,[],[f2,f19]) ).
fof(f28,plain,
! [X0,X1] : multiply(X1,add(X1,X0)) = add(X1,multiply(X0,X1)),
inference(superposition,[],[f2,f19]) ).
fof(f29,plain,
! [X0,X1] : add(X0,X1) = add(X1,multiply(X0,X0)),
inference(superposition,[],[f5,f19]) ).
fof(f30,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[],[f29,f19]) ).
fof(f32,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(forward_demodulation,[],[f27,f4]) ).
fof(f35,plain,
! [X0,X1] : add(X1,multiply(X0,X1)) = X1,
inference(backward_demodulation,[],[f4,f30]) ).
fof(f37,plain,
! [X0,X1] : multiply(X1,add(X1,X0)) = X1,
inference(backward_demodulation,[],[f28,f35]) ).
fof(f43,plain,
! [X2,X0,X1] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X2,multiply(X0,X1)),X1),
inference(superposition,[],[f5,f35]) ).
fof(f44,plain,
! [X2,X0,X1] : add(multiply(X0,X1),multiply(X1,X2)) = multiply(X1,add(X2,multiply(X0,X1))),
inference(superposition,[],[f5,f35]) ).
fof(f45,plain,
! [X2,X0,X1] : multiply(X1,add(X0,X2)) = multiply(add(X2,multiply(X0,X1)),X1),
inference(forward_demodulation,[],[f43,f2]) ).
fof(f58,plain,
! [X0,X1] : multiply(X1,add(X0,X1)) = add(X1,multiply(X1,X0)),
inference(superposition,[],[f44,f19]) ).
fof(f71,plain,
! [X0,X1] : add(X1,multiply(X1,X0)) = X1,
inference(forward_demodulation,[],[f58,f32]) ).
fof(f77,plain,
! [X0] : multiply(X0,n1) = X0,
inference(superposition,[],[f37,f3]) ).
fof(f92,plain,
! [X0,X1] : add(inverse(X0),multiply(X1,X0)) = add(X1,inverse(X0)),
inference(backward_demodulation,[],[f13,f77]) ).
fof(f132,plain,
! [X0,X1] : add(n0,multiply(inverse(X1),X0)) = multiply(inverse(X1),add(X0,n0)),
inference(superposition,[],[f44,f6]) ).
fof(f166,plain,
! [X0] : add(X0,n0) = X0,
inference(superposition,[],[f71,f6]) ).
fof(f169,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,add(X1,multiply(X1,X0))),
inference(superposition,[],[f2,f71]) ).
fof(f176,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,X1),
inference(forward_demodulation,[],[f169,f71]) ).
fof(f178,plain,
! [X0,X1] : multiply(inverse(X1),X0) = add(n0,multiply(inverse(X1),X0)),
inference(backward_demodulation,[],[f132,f166]) ).
fof(f184,plain,
! [X2,X0,X1] : multiply(X1,add(X0,X2)) = multiply(X1,add(X2,multiply(X0,X1))),
inference(backward_demodulation,[],[f45,f176]) ).
fof(f191,plain,
multiply(a,multiply(b,c)) != multiply(c,multiply(a,b)),
inference(backward_demodulation,[],[f7,f176]) ).
fof(f197,plain,
! [X2,X0,X1] : multiply(X1,add(X0,X2)) = add(multiply(X0,X1),multiply(X1,X2)),
inference(backward_demodulation,[],[f44,f184]) ).
fof(f229,plain,
! [X0,X1] : add(n0,multiply(inverse(X1),X0)) = multiply(inverse(X1),add(X1,X0)),
inference(superposition,[],[f197,f6]) ).
fof(f245,plain,
! [X0,X1] : multiply(inverse(X1),X0) = multiply(inverse(X1),add(X1,X0)),
inference(forward_demodulation,[],[f229,f178]) ).
fof(f440,plain,
! [X0,X1] : multiply(inverse(X1),multiply(X0,X1)) = multiply(inverse(X1),X1),
inference(superposition,[],[f245,f35]) ).
fof(f473,plain,
! [X0,X1] : multiply(X1,inverse(X1)) = multiply(inverse(X1),multiply(X0,X1)),
inference(forward_demodulation,[],[f440,f176]) ).
fof(f477,plain,
! [X0,X1] : n0 = multiply(inverse(X1),multiply(X0,X1)),
inference(forward_demodulation,[],[f473,f6]) ).
fof(f547,plain,
! [X0] : add(n0,X0) = X0,
inference(superposition,[],[f166,f30]) ).
fof(f623,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),add(inverse(X1),X2)) = add(n0,multiply(X2,multiply(X0,X1))),
inference(superposition,[],[f2,f477]) ).
fof(f624,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),add(X2,inverse(X1))) = add(multiply(X2,multiply(X0,X1)),n0),
inference(superposition,[],[f2,f477]) ).
fof(f641,plain,
! [X2,X0,X1] : add(n0,multiply(X2,multiply(X0,X1))) = multiply(multiply(X0,X1),add(X2,inverse(X1))),
inference(forward_demodulation,[],[f624,f30]) ).
fof(f642,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(multiply(X0,X1),add(inverse(X1),X2)),
inference(forward_demodulation,[],[f623,f547]) ).
fof(f659,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(multiply(X0,X1),add(X2,inverse(X1))),
inference(forward_demodulation,[],[f641,f547]) ).
fof(f730,plain,
! [X2,X0,X1] : multiply(multiply(X1,X0),multiply(X2,X0)) = multiply(multiply(X2,X0),add(X1,inverse(X0))),
inference(superposition,[],[f642,f92]) ).
fof(f769,plain,
! [X2,X0,X1] : multiply(X1,multiply(X2,X0)) = multiply(multiply(X1,X0),multiply(X2,X0)),
inference(forward_demodulation,[],[f730,f659]) ).
fof(f927,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(multiply(X0,X1),multiply(X2,X1)),
inference(superposition,[],[f176,f769]) ).
fof(f1118,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(superposition,[],[f769,f927]) ).
fof(f1150,plain,
multiply(a,multiply(b,c)) != multiply(a,multiply(c,b)),
inference(backward_demodulation,[],[f191,f1118]) ).
fof(f1176,plain,
multiply(a,multiply(b,c)) != multiply(a,multiply(b,c)),
inference(forward_demodulation,[],[f1150,f176]) ).
fof(f1177,plain,
$false,
inference(trivial_inequality_removal,[],[f1176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n013.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:03:51 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 7.34/1.58 % (1579082)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.34/1.58 % (1579092)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1445883268:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.34/1.58 % (1579087)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=515259308:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.34/1.58 % (1579089)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=29228349:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.34/1.58 % (1579091)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3199635423:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.34/1.58 % (1579090)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=431367986:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.34/1.58 % (1579088)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=675581985:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.34/1.58 % (1579093)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=243628861:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.34/1.58 % (1579092)Instruction limit reached!
% 7.34/1.58 % (1579092)------------------------------
% 7.34/1.58 % (1579092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/1.58 % (1579092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/1.58 % (1579092)CaDiCaL version: 2.1.3
% 7.34/1.58 % (1579092)Termination reason: Instruction limit
% 7.34/1.58 % (1579092)Termination phase: Saturation
% 7.34/1.58 % (1579092)Time elapsed: 0.091 s
% 7.34/1.58 % (1579092)Peak memory usage: 90 MB
% 7.34/1.58 % (1579092)Instructions burned: 258 (million)
% 7.34/1.58 % (1579090)Instruction limit reached!
% 7.34/1.58 % (1579090)------------------------------
% 7.34/1.58 % (1579090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/1.58 % (1579090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/1.58 % (1579090)CaDiCaL version: 2.1.3
% 7.34/1.58 % (1579090)Termination reason: Instruction limit
% 7.34/1.58 % (1579090)Termination phase: Saturation
% 7.34/1.58 % (1579090)Time elapsed: 0.092 s
% 7.34/1.58 % (1579090)Peak memory usage: 88 MB
% 7.34/1.58 % (1579090)Instructions burned: 137 (million)
% 7.34/1.58 % (1579091)Instruction limit reached!
% 7.34/1.58 % (1579091)------------------------------
% 7.34/1.58 % (1579091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/1.58 % (1579091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/1.58 % (1579091)CaDiCaL version: 2.1.3
% 7.34/1.58 % (1579091)Termination reason: Instruction limit
% 7.34/1.58 % (1579091)Termination phase: Saturation
% 7.34/1.58 % (1579091)Time elapsed: 0.104 s
% 7.34/1.58 % (1579091)Peak memory usage: 89 MB
% 7.34/1.58 % (1579091)Instructions burned: 182 (million)
% 7.34/1.58 % (1579166)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1079584241:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 7.34/1.58 % (1579171)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2558805107:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 7.34/1.58 % (1579175)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2150781523:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 7.34/1.58 % (1579175)Instruction limit reached!
% 7.34/1.58 % (1579175)------------------------------
% 7.34/1.58 % (1579175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/1.58 % (1579175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/1.58 % (1579175)CaDiCaL version: 2.1.3
% 7.34/1.58 % (1579175)Termination reason: Instruction limit
% 7.34/1.58 % (1579175)Termination phase: Saturation
% 7.34/1.58 % (1579175)Time elapsed: 0.099 s
% 8.38/1.78 % (1579175)Peak memory usage: 92 MB
% 8.38/1.78 % (1579175)Instructions burned: 216 (million)
% 8.38/1.78 % (1579244)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=2382901823:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 8.38/1.78 % (1579093)Instruction limit reached!
% 8.38/1.78 % (1579093)------------------------------
% 8.38/1.78 % (1579093)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.38/1.78 % (1579093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.38/1.78 % (1579093)CaDiCaL version: 2.1.3
% 8.38/1.78 % (1579093)Termination reason: Instruction limit
% 8.38/1.78 % (1579093)Termination phase: Saturation
% 8.38/1.78 % (1579093)Time elapsed: 0.680 s
% 8.38/1.78 % (1579093)Peak memory usage: 98 MB
% 8.38/1.78 % (1579093)Instructions burned: 1188 (million)
% 8.38/1.78 % (1579166)First to succeed.
% 8.38/1.78 % (1579166)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1579082"
% 8.38/1.78 % (1579244)Instruction limit reached!
% 8.38/1.78 % (1579244)------------------------------
% 8.38/1.78 % (1579244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.38/1.78 % (1579244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.38/1.78 % (1579244)CaDiCaL version: 2.1.3
% 8.38/1.78 % (1579244)Termination reason: Instruction limit
% 8.38/1.78 % (1579244)Termination phase: Saturation
% 8.38/1.78 % (1579244)Time elapsed: 0.201 s
% 8.38/1.78 % (1579244)Peak memory usage: 94 MB
% 8.38/1.78 % (1579244)Instructions burned: 317 (million)
% 8.38/1.78 % (1579088)Also succeeded, but the first one will report.
% 8.38/1.78 % (1579339)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2232462870:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 8.38/1.78 % (1579349)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2496588007:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 8.38/1.78 % (1579166)Refutation found. Thanks to Tanya!
% 8.38/1.78 % SZS status Unsatisfiable for theBenchmark
% 8.38/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 8.38/1.78 % (1579166)------------------------------
% 8.38/1.78 % (1579166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.38/1.78 % (1579166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.38/1.78 % (1579166)CaDiCaL version: 2.1.3
% 8.38/1.78 % (1579166)Termination reason: Refutation
% 8.38/1.78 % (1579166)Time elapsed: 0.544 s
% 8.38/1.78 % (1579166)Peak memory usage: 130 MB
% 8.38/1.78 % (1579166)Instructions burned: 1124 (million)
% 8.38/1.78 % (1579166)------------------------------
% 8.38/1.78 % (1579166)------------------------------
% 8.38/1.78 % (1579082)Success in time 1.144 s
% 8.38/1.78 % Vampire exiting
%------------------------------------------------------------------------------