%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO034-1 : 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 : n014.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 09:35:57 AM UTC 2026
% Result : Unsatisfiable 2.84s 1.16s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_1) ).
fof(f3,axiom,
! [X0,X1] : multiply(X0,X0,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_2) ).
fof(f5,axiom,
! [X0,X1] : multiply(X0,X1,inverse(X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f6,negated_conjecture,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_single_axiom) ).
fof(f7,plain,
b != multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)),
inference(reorient_equations,[],[f6]) ).
fof(f8,plain,
! [X2,X3,X0,X1] : multiply(X1,X0,multiply(X0,X2,X3)) = multiply(X0,X2,multiply(X1,X0,X3)),
inference(superposition,[],[f1,f2]) ).
fof(f11,plain,
! [X2,X3,X0,X1] : multiply(X0,X1,multiply(inverse(X1),X2,X3)) = multiply(X0,X2,multiply(X0,X1,X3)),
inference(superposition,[],[f1,f5]) ).
fof(f19,plain,
! [X2,X3,X0,X1] : multiply(X0,X1,X2) = multiply(X0,X1,multiply(X2,multiply(X0,X1,X2),X3)),
inference(superposition,[],[f1,f3]) ).
fof(f20,plain,
b != multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),
inference(superposition,[],[f7,f1]) ).
fof(f34,plain,
! [X2,X0,X1] : multiply(X1,X2,X0) = multiply(X2,X0,multiply(X1,X2,X0)),
inference(superposition,[],[f8,f2]) ).
fof(f104,plain,
! [X0,X1] : multiply(X1,inverse(X1),X0) = X0,
inference(superposition,[],[f34,f5]) ).
fof(f118,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f104,f5]) ).
fof(f129,plain,
b != multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),
inference(superposition,[],[f20,f104]) ).
fof(f136,plain,
! [X0,X1] : multiply(X1,inverse(X0),X0) = X1,
inference(superposition,[],[f5,f118]) ).
fof(f580,plain,
! [X2,X0,X1] : multiply(X0,X1,multiply(inverse(X1),X0,X2)) = X0,
inference(superposition,[],[f19,f5]) ).
fof(f663,plain,
! [X0,X1] : multiply(inverse(X0),X1,X0) = X1,
inference(superposition,[],[f580,f34]) ).
fof(f693,plain,
! [X0,X1] : multiply(X0,X1,inverse(X0)) = X1,
inference(superposition,[],[f663,f118]) ).
fof(f748,plain,
! [X2,X0,X1] : multiply(X1,X2,X0) = multiply(X2,X0,multiply(X1,X2,inverse(X2))),
inference(superposition,[],[f8,f693]) ).
fof(f768,plain,
! [X2,X0,X1] : multiply(X1,X2,X0) = multiply(X2,X0,X1),
inference(forward_demodulation,[],[f748,f5]) ).
fof(f894,plain,
b != multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(e,g,f),c)),
inference(superposition,[],[f129,f768]) ).
fof(f899,plain,
b != multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(c,d,multiply(e,g,f))),
inference(forward_demodulation,[],[f894,f768]) ).
fof(f1379,plain,
! [X2,X0,X1] : multiply(X1,X2,X0) = multiply(X1,X0,multiply(inverse(X0),X2,X0)),
inference(superposition,[],[f11,f2]) ).
fof(f1535,plain,
! [X2,X0,X1] : multiply(X1,X2,X0) = multiply(X1,X0,multiply(X0,inverse(X0),X2)),
inference(forward_demodulation,[],[f1379,f768]) ).
fof(f1574,plain,
! [X2,X0,X1] : multiply(X1,X0,X2) = multiply(X1,X2,X0),
inference(forward_demodulation,[],[f1535,f104]) ).
fof(f1733,plain,
b != multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(c,d,multiply(e,f,g))),
inference(superposition,[],[f899,f1574]) ).
fof(f1742,plain,
$false,
inference(forward_subsumption_resolution,[],[f1733,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n014.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Mon Sep 28 21:04:30 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running first-order theorem proving
% 0.12/0.21 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
% 2.84/1.16 % (2186879)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.84/1.16 % (2186890)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2403828764:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.84/1.16 % (2186890)First to succeed.
% 2.84/1.16 % (2186890)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2186879"
% 2.84/1.16 % (2186889)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2824296816:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.84/1.16 % (2186884)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=1757989286:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.84/1.16 % (2186885)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=188910683:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.84/1.16 % (2186888)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=867873393:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.84/1.16 % (2186886)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=853351022:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.84/1.16 % (2186887)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1847985932:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.84/1.16 % (2186887)Instruction limit reached!
% 2.84/1.16 % (2186887)------------------------------
% 2.84/1.16 % (2186887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.16 % (2186887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.16 % (2186887)CaDiCaL version: 2.1.3
% 2.84/1.16 % (2186887)Termination reason: Instruction limit
% 2.84/1.16 % (2186887)Termination phase: Saturation
% 2.84/1.16 % (2186887)Time elapsed: 0.085 s
% 2.84/1.16 % (2186887)Peak memory usage: 88 MB
% 2.84/1.16 % (2186887)Instructions burned: 136 (million)
% 2.84/1.16 % (2186888)Instruction limit reached!
% 2.84/1.16 % (2186888)------------------------------
% 2.84/1.16 % (2186888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.16 % (2186888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.16 % (2186888)CaDiCaL version: 2.1.3
% 2.84/1.16 % (2186888)Termination reason: Instruction limit
% 2.84/1.16 % (2186888)Termination phase: Saturation
% 2.84/1.16 % (2186888)Time elapsed: 0.109 s
% 2.84/1.16 % (2186888)Peak memory usage: 89 MB
% 2.84/1.16 % (2186888)Instructions burned: 181 (million)
% 2.84/1.16 % (2186890)Refutation found. Thanks to Tanya!
% 2.84/1.16 % SZS status Unsatisfiable for theBenchmark
% 2.84/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.84/1.16 % (2186890)------------------------------
% 2.84/1.16 % (2186890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.16 % (2186890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.16 % (2186890)CaDiCaL version: 2.1.3
% 2.84/1.16 % (2186890)Termination reason: Refutation
% 2.84/1.16 % (2186890)Time elapsed: 0.022 s
% 2.84/1.16 % (2186890)Peak memory usage: 88 MB
% 2.84/1.16 % (2186890)Instructions burned: 66 (million)
% 2.84/1.16 % (2186890)------------------------------
% 2.84/1.16 % (2186890)------------------------------
% 2.84/1.16 % (2186879)Success in time 0.304 s
% 2.84/1.16 % Vampire exiting
%------------------------------------------------------------------------------