%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO074-1 : TPTP v9.3.1. Released v2.6.0.
% 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 09:36:01 AM UTC 2026
% Result : Unsatisfiable 6.76s 1.72s
% Output : Refutation 6.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : inverse(add(inverse(add(inverse(add(X0,X1)),X2)),inverse(add(X0,inverse(add(inverse(X2),inverse(add(X2,X3)))))))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dn1) ).
fof(f2,negated_conjecture,
add(inverse(add(inverse(a),b)),inverse(add(inverse(a),inverse(b)))) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',huntinton_3) ).
fof(f3,plain,
a != add(inverse(add(inverse(a),b)),inverse(add(inverse(a),inverse(b)))),
inference(reorient_equations,[],[f2]) ).
fof(f4,plain,
! [X2,X0,X1,X4,X5] : inverse(add(inverse(add(X0,X4)),inverse(add(inverse(add(inverse(add(X1,X2)),X0)),inverse(add(inverse(X4),inverse(add(X4,X5)))))))) = X4,
inference(superposition,[],[f1,f1]) ).
fof(f5,plain,
! [X2,X3,X0,X1,X4] : inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3)))))) = inverse(add(X0,inverse(add(inverse(add(X1,X2)),inverse(add(inverse(inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3))))))),inverse(add(inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3)))))),X4)))))))),
inference(superposition,[],[f1,f1]) ).
fof(f8,plain,
! [X2,X0,X1] : inverse(X0) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X0)),X1)),X0)),X2)),inverse(X0))),X0)),
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
! [X0] : inverse(X0) = inverse(add(inverse(add(X0,inverse(X0))),X0)),
inference(superposition,[],[f8,f1]) ).
fof(f12,plain,
! [X2,X3,X0,X1] : inverse(add(inverse(X0),inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X0)),X1)),X0)),X2)),inverse(add(inverse(X0),inverse(add(X0,X3)))))))) = X0,
inference(superposition,[],[f1,f8]) ).
fof(f20,plain,
! [X0,X1] : inverse(add(inverse(X0),inverse(add(X0,inverse(add(inverse(X0),inverse(add(X0,X1)))))))) = X0,
inference(superposition,[],[f1,f9]) ).
fof(f35,plain,
! [X2,X0,X1] : inverse(add(inverse(add(inverse(add(X1,X2)),X0)),inverse(add(X1,X0)))) = X0,
inference(superposition,[],[f1,f20]) ).
fof(f65,plain,
! [X2,X0] : inverse(add(inverse(add(X0,X2)),inverse(add(inverse(X0),X2)))) = X2,
inference(superposition,[],[f35,f20]) ).
fof(f107,plain,
! [X0] : inverse(add(inverse(add(add(X0,inverse(X0)),X0)),inverse(X0))) = X0,
inference(superposition,[],[f65,f9]) ).
fof(f168,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(add(X0,X1)),X0)),inverse(add(X0,X1)))) = X0,
inference(superposition,[],[f4,f35]) ).
fof(f198,plain,
! [X0] : inverse(X0) = inverse(add(X0,inverse(add(add(X0,inverse(X0)),inverse(X0))))),
inference(superposition,[],[f35,f107]) ).
fof(f240,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(X0),X1)),inverse(add(X0,X1)))) = X1,
inference(superposition,[],[f35,f198]) ).
fof(f364,plain,
! [X0] : inverse(add(inverse(add(inverse(X0),X0)),inverse(X0))) = X0,
inference(superposition,[],[f4,f168]) ).
fof(f555,plain,
! [X0] : inverse(X0) = inverse(add(X0,inverse(add(inverse(X0),inverse(X0))))),
inference(superposition,[],[f35,f364]) ).
fof(f671,plain,
! [X0] : inverse(add(inverse(X0),inverse(add(X0,inverse(add(inverse(X0),inverse(X0))))))) = X0,
inference(superposition,[],[f20,f555]) ).
fof(f691,plain,
! [X0] : inverse(add(inverse(X0),inverse(X0))) = X0,
inference(forward_demodulation,[],[f671,f555]) ).
fof(f710,plain,
! [X0] : inverse(add(inverse(X0),inverse(X0))) = add(X0,inverse(add(inverse(X0),inverse(X0)))),
inference(superposition,[],[f691,f555]) ).
fof(f754,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f710,f691]) ).
fof(f760,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f691,f754]) ).
fof(f781,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(add(X0,X1)),X0)),inverse(X0))) = X0,
inference(superposition,[],[f35,f754]) ).
fof(f796,plain,
! [X0,X1] : inverse(X0) = add(inverse(add(inverse(X1),X0)),inverse(add(X1,X0))),
inference(superposition,[],[f760,f240]) ).
fof(f799,plain,
! [X0,X1] : inverse(X0) = add(inverse(add(X1,X0)),inverse(add(inverse(X1),X0))),
inference(superposition,[],[f760,f65]) ).
fof(f836,plain,
! [X2,X3,X0,X1,X4] : inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3)))))) = inverse(add(X0,inverse(add(inverse(add(X1,X2)),inverse(add(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3))))),inverse(add(inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3)))))),X4)))))))),
inference(forward_demodulation,[],[f5,f760]) ).
fof(f3388,plain,
! [X0,X1] : inverse(add(X0,X1)) = inverse(add(X0,inverse(inverse(add(X0,X1))))),
inference(superposition,[],[f781,f168]) ).
fof(f3390,plain,
! [X0,X1] : inverse(add(X1,X0)) = inverse(add(X0,inverse(inverse(add(X1,X0))))),
inference(superposition,[],[f781,f35]) ).
fof(f3533,plain,
! [X0,X1] : inverse(add(X1,X0)) = inverse(add(X0,add(X1,X0))),
inference(forward_demodulation,[],[f3390,f760]) ).
fof(f3535,plain,
! [X0,X1] : inverse(add(X0,X1)) = inverse(add(X0,add(X0,X1))),
inference(forward_demodulation,[],[f3388,f760]) ).
fof(f4545,plain,
! [X0,X1] : inverse(inverse(X0)) = inverse(add(inverse(add(X1,X0)),inverse(X0))),
inference(superposition,[],[f3533,f796]) ).
fof(f4552,plain,
! [X0,X1] : inverse(add(inverse(add(X1,X0)),inverse(X0))) = X0,
inference(forward_demodulation,[],[f4545,f760]) ).
fof(f5877,plain,
! [X2,X3,X0,X1] : inverse(add(inverse(X0),inverse(add(inverse(add(inverse(add(inverse(add(X0,X1)),X0)),X2)),inverse(add(inverse(X0),inverse(add(X0,X3)))))))) = X0,
inference(forward_demodulation,[],[f12,f760]) ).
fof(f6069,plain,
! [X0,X1] : inverse(add(inverse(X0),add(inverse(X0),inverse(add(X0,X1))))) = X0,
inference(superposition,[],[f5877,f4552]) ).
fof(f6182,plain,
! [X0,X1] : inverse(add(inverse(X0),inverse(add(X0,X1)))) = X0,
inference(forward_demodulation,[],[f6069,f3535]) ).
fof(f6544,plain,
! [X0,X1] : inverse(X0) = add(inverse(X0),inverse(add(X0,X1))),
inference(superposition,[],[f760,f6182]) ).
fof(f7073,plain,
! [X0,X1] : add(X0,inverse(add(inverse(X0),X1))) = X0,
inference(superposition,[],[f6544,f760]) ).
fof(f7502,plain,
! [X2,X0,X1,X4] : inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))) = inverse(add(X1,inverse(add(inverse(X0),inverse(add(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2))))),inverse(add(inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))),X4)))))))),
inference(superposition,[],[f836,f7073]) ).
fof(f7528,plain,
! [X2,X0,X1] : inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))) = inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))))))),
inference(forward_demodulation,[],[f7502,f7073]) ).
fof(f7610,plain,
! [X2,X0,X1] : inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))) = inverse(add(X1,X0)),
inference(forward_demodulation,[],[f7528,f6182]) ).
fof(f7623,plain,
! [X0,X1] : inverse(add(X0,X1)) = inverse(add(X1,X0)),
inference(forward_demodulation,[],[f7610,f6182]) ).
fof(f8386,plain,
a != add(inverse(add(b,inverse(a))),inverse(add(inverse(a),inverse(b)))),
inference(superposition,[],[f3,f7623]) ).
fof(f10719,plain,
! [X0,X1] : inverse(X0) = add(inverse(add(X1,X0)),inverse(add(X0,inverse(X1)))),
inference(superposition,[],[f799,f7623]) ).
fof(f16694,plain,
a != inverse(inverse(a)),
inference(superposition,[],[f8386,f10719]) ).
fof(f16864,plain,
$false,
inference(forward_subsumption_resolution,[],[f16694,f760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO074-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:08:50 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 6.05/1.53 % (562340)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.05/1.53 % (562345)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=2436444137:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.05/1.53 % (562348)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2581523502:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.05/1.53 % (562347)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2898468385:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.05/1.53 % (562351)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1998006231:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.05/1.53 % (562346)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=4265150828:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.05/1.53 % (562349)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3043500856:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.05/1.53 % (562350)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4252526673:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.05/1.53 % (562348)Instruction limit reached!
% 6.05/1.53 % (562348)------------------------------
% 6.05/1.53 % (562348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.53 % (562348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.53 % (562348)CaDiCaL version: 2.1.3
% 6.05/1.53 % (562348)Termination reason: Instruction limit
% 6.05/1.53 % (562348)Termination phase: Saturation
% 6.05/1.53 % (562348)Time elapsed: 0.079 s
% 6.05/1.53 % (562348)Peak memory usage: 89 MB
% 6.05/1.53 % (562348)Instructions burned: 138 (million)
% 6.05/1.53 % (562349)Instruction limit reached!
% 6.05/1.53 % (562349)------------------------------
% 6.05/1.53 % (562349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.53 % (562349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.53 % (562349)CaDiCaL version: 2.1.3
% 6.05/1.53 % (562349)Termination reason: Instruction limit
% 6.05/1.53 % (562349)Termination phase: Saturation
% 6.05/1.53 % (562349)Time elapsed: 0.094 s
% 6.05/1.53 % (562349)Peak memory usage: 89 MB
% 6.05/1.53 % (562349)Instructions burned: 181 (million)
% 6.05/1.53 % (562350)Instruction limit reached!
% 6.05/1.53 % (562350)------------------------------
% 6.05/1.53 % (562350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.53 % (562350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.53 % (562350)CaDiCaL version: 2.1.3
% 6.05/1.53 % (562350)Termination reason: Instruction limit
% 6.05/1.53 % (562350)Termination phase: Saturation
% 6.05/1.53 % (562350)Time elapsed: 0.155 s
% 6.05/1.53 % (562350)Peak memory usage: 89 MB
% 6.05/1.53 % (562350)Instructions burned: 258 (million)
% 6.05/1.53 % (562359)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1796801078:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 6.05/1.53 % (562360)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2809892132:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.05/1.53 % (562361)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3747934854:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.05/1.53 % (562361)Instruction limit reached!
% 6.05/1.53 % (562361)------------------------------
% 6.05/1.53 % (562361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.53 % (562361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.53 % (562361)CaDiCaL version: 2.1.3
% 6.05/1.53 % (562361)Termination reason: Instruction limit
% 6.05/1.53 % (562361)Termination phase: Saturation
% 6.05/1.53 % (562361)Time elapsed: 0.089 s
% 6.05/1.53 % (562361)Peak memory usage: 99 MB
% 6.76/1.72 % (562361)Instructions burned: 215 (million)
% 6.76/1.72 % (562351)First to succeed.
% 6.76/1.72 % (562351)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-562340"
% 6.76/1.72 % (562365)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=3175398888: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)
% 6.76/1.72 % (562345)Also succeeded, but the first one will report.
% 6.76/1.72 % (562365)Instruction limit reached!
% 6.76/1.72 % (562365)------------------------------
% 6.76/1.72 % (562365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/1.72 % (562365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.72 % (562365)CaDiCaL version: 2.1.3
% 6.76/1.72 % (562365)Termination reason: Instruction limit
% 6.76/1.72 % (562365)Termination phase: Saturation
% 6.76/1.72 % (562365)Time elapsed: 0.188 s
% 6.76/1.72 % (562365)Peak memory usage: 95 MB
% 6.76/1.72 % (562365)Instructions burned: 317 (million)
% 6.76/1.72 % (562351)Refutation found. Thanks to Tanya!
% 6.76/1.72 % SZS status Unsatisfiable for theBenchmark
% 6.76/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 6.76/1.72 % (562351)------------------------------
% 6.76/1.72 % (562351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/1.72 % (562351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.72 % (562351)CaDiCaL version: 2.1.3
% 6.76/1.72 % (562351)Termination reason: Refutation
% 6.76/1.72 % (562351)Time elapsed: 0.466 s
% 6.76/1.72 % (562351)Peak memory usage: 97 MB
% 6.76/1.72 % (562351)Instructions burned: 858 (million)
% 6.76/1.72 % (562351)------------------------------
% 6.76/1.72 % (562351)------------------------------
% 6.76/1.72 % (562340)Success in time 0.865 s
% 6.76/1.72 % Vampire exiting
%------------------------------------------------------------------------------