%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 10:13:13 AM UTC 2026
% Result : Unsatisfiable 8.39s 2.15s
% Output : Refutation 8.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_3) ).
fof(f21,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_4) ).
fof(f22,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_5) ).
fof(f23,axiom,
! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_6) ).
fof(f25,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p12x) ).
fof(f26,plain,
least_upper_bound(b,c) = least_upper_bound(c,a),
inference(backward_demodulation,[],[f22,f6]) ).
fof(f27,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(c,a),
inference(backward_demodulation,[],[f21,f5]) ).
fof(f28,plain,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(forward_demodulation,[],[f26,f6]) ).
fof(f29,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(forward_demodulation,[],[f27,f5]) ).
fof(f36,plain,
! [X0,X1] : least_upper_bound(X0,inverse(X1)) = inverse(greatest_lower_bound(inverse(X0),X1)),
inference(superposition,[],[f23,f19]) ).
fof(f80,plain,
! [X0,X1] : inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1)),
inference(superposition,[],[f20,f19]) ).
fof(f81,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[],[f20,f19]) ).
fof(f207,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f3,f19]) ).
fof(f212,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f213,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f212,f1]) ).
fof(f216,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f213,f19]) ).
fof(f276,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(superposition,[],[f14,f3]) ).
fof(f287,plain,
! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0)),
inference(forward_demodulation,[],[f276,f5]) ).
fof(f294,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f3]) ).
fof(f326,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),identity),
inference(superposition,[],[f213,f207]) ).
fof(f369,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f1]) ).
fof(f402,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f326,f19]) ).
fof(f429,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(superposition,[],[f13,f402]) ).
fof(f841,plain,
! [X0,X1] : least_upper_bound(X0,inverse(multiply(X1,inverse(X0)))) = inverse(multiply(greatest_lower_bound(identity,X1),inverse(X0))),
inference(superposition,[],[f36,f369]) ).
fof(f843,plain,
! [X0,X1] : least_upper_bound(X0,inverse(multiply(X1,inverse(X0)))) = multiply(X0,inverse(greatest_lower_bound(identity,X1))),
inference(forward_demodulation,[],[f841,f80]) ).
fof(f857,plain,
! [X0,X1] : multiply(X0,inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X0,multiply(X0,inverse(X1))),
inference(forward_demodulation,[],[f843,f80]) ).
fof(f864,plain,
! [X0,X1] : multiply(X0,inverse(greatest_lower_bound(identity,X1))) = multiply(X0,least_upper_bound(identity,inverse(X1))),
inference(forward_demodulation,[],[f857,f429]) ).
fof(f880,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[],[f216,f20]) ).
fof(f1146,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(greatest_lower_bound(X1,X0),inverse(greatest_lower_bound(identity,multiply(inverse(X0),X1)))),
inference(superposition,[],[f880,f287]) ).
fof(f1180,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(greatest_lower_bound(X1,X0),least_upper_bound(identity,inverse(multiply(inverse(X0),X1)))),
inference(forward_demodulation,[],[f1146,f864]) ).
fof(f1198,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(greatest_lower_bound(X1,X0),least_upper_bound(identity,multiply(inverse(X1),X0))),
inference(forward_demodulation,[],[f1180,f81]) ).
fof(f1211,plain,
! [X0,X1] : multiply(greatest_lower_bound(X1,X0),least_upper_bound(identity,multiply(inverse(X1),X0))) = X0,
inference(forward_demodulation,[],[f1198,f19]) ).
fof(f1427,plain,
b = multiply(greatest_lower_bound(c,a),least_upper_bound(identity,multiply(inverse(c),b))),
inference(superposition,[],[f1211,f29]) ).
fof(f1438,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,X1),multiply(inverse(X0),least_upper_bound(X0,X1))) = X1,
inference(superposition,[],[f1211,f294]) ).
fof(f1466,plain,
b = multiply(greatest_lower_bound(c,a),multiply(inverse(c),least_upper_bound(c,b))),
inference(forward_demodulation,[],[f1427,f294]) ).
fof(f1482,plain,
b = multiply(greatest_lower_bound(c,a),multiply(inverse(c),least_upper_bound(c,a))),
inference(forward_demodulation,[],[f1466,f28]) ).
fof(f1492,plain,
a = b,
inference(forward_demodulation,[],[f1482,f1438]) ).
fof(f1501,plain,
$false,
inference(forward_subsumption_resolution,[],[f1492,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n006.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 09:35:56 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 5.56/1.96 % (2733870)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.56/1.96 % (2733879)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=440799867:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.56/1.96 % (2733881)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=395540000:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.56/1.96 % (2733878)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3304832645:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.56/1.96 % (2733877)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2480084630:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.56/1.96 % (2733876)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=2583094828:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.56/1.96 % (2733875)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=560424743:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.56/1.96 % (2733880)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2753430173:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.56/1.96 % (2733879)Instruction limit reached!
% 5.56/1.96 % (2733879)------------------------------
% 5.56/1.96 % (2733879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.96 % (2733879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.96 % (2733879)CaDiCaL version: 2.1.3
% 5.56/1.96 % (2733879)Termination reason: Instruction limit
% 5.56/1.96 % (2733879)Termination phase: Saturation
% 5.56/1.96 % (2733879)Time elapsed: 0.056 s
% 5.56/1.96 % (2733879)Peak memory usage: 89 MB
% 5.56/1.96 % (2733879)Instructions burned: 183 (million)
% 5.56/1.96 % (2733878)Instruction limit reached!
% 5.56/1.96 % (2733878)------------------------------
% 5.56/1.96 % (2733878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.96 % (2733878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.96 % (2733878)CaDiCaL version: 2.1.3
% 5.56/1.96 % (2733878)Termination reason: Instruction limit
% 5.56/1.96 % (2733878)Termination phase: Saturation
% 5.56/1.96 % (2733878)Time elapsed: 0.083 s
% 5.56/1.96 % (2733878)Peak memory usage: 88 MB
% 5.56/1.96 % (2733878)Instructions burned: 137 (million)
% 5.56/1.96 % (2733889)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3397250805:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 5.56/1.96 % (2733880)Instruction limit reached!
% 5.56/1.96 % (2733880)------------------------------
% 5.56/1.96 % (2733880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.96 % (2733880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.96 % (2733880)CaDiCaL version: 2.1.3
% 5.56/1.96 % (2733880)Termination reason: Instruction limit
% 5.56/1.96 % (2733880)Termination phase: Saturation
% 5.56/1.96 % (2733880)Time elapsed: 0.163 s
% 5.56/1.96 % (2733880)Peak memory usage: 90 MB
% 5.56/1.96 % (2733880)Instructions burned: 258 (million)
% 5.56/1.96 % (2733890)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1104142062:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.56/1.96 % (2733892)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=577155681:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.56/1.96 % (2733892)Instruction limit reached!
% 5.56/1.96 % (2733892)------------------------------
% 5.56/1.96 % (2733892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.96 % (2733892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.96 % (2733892)CaDiCaL version: 2.1.3
% 5.56/1.96 % (2733892)Termination reason: Instruction limit
% 5.56/1.96 % (2733892)Termination phase: Saturation
% 5.56/1.96 % (2733892)Time elapsed: 0.118 s
% 8.39/2.15 % (2733892)Peak memory usage: 92 MB
% 8.39/2.15 % (2733892)Instructions burned: 215 (million)
% 8.39/2.15 % (2733895)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=471557812: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)
% 8.39/2.15 % (2733895)Instruction limit reached!
% 8.39/2.15 % (2733895)------------------------------
% 8.39/2.15 % (2733895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.15 % (2733895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.15 % (2733895)CaDiCaL version: 2.1.3
% 8.39/2.15 % (2733895)Termination reason: Instruction limit
% 8.39/2.15 % (2733895)Termination phase: Saturation
% 8.39/2.15 % (2733895)Time elapsed: 0.088 s
% 8.39/2.15 % (2733895)Peak memory usage: 90 MB
% 8.39/2.15 % (2733895)Instructions burned: 318 (million)
% 8.39/2.15 % (2733881)Instruction limit reached!
% 8.39/2.15 % (2733881)------------------------------
% 8.39/2.15 % (2733881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.15 % (2733881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.15 % (2733881)CaDiCaL version: 2.1.3
% 8.39/2.15 % (2733881)Termination reason: Instruction limit
% 8.39/2.15 % (2733881)Termination phase: Saturation
% 8.39/2.15 % (2733881)Time elapsed: 0.643 s
% 8.39/2.15 % (2733881)Peak memory usage: 99 MB
% 8.39/2.15 % (2733881)Instructions burned: 1187 (million)
% 8.39/2.15 % (2733889)First to succeed.
% 8.39/2.15 % (2733889)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2733870"
% 8.39/2.15 % (2733897)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=611515233:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 8.39/2.15 % (2733898)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1140706963:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2992 on theBenchmark for (2992ds/2836Mi)
% 8.39/2.15 % (2733876)Also succeeded, but the first one will report.
% 8.39/2.15 % (2733890)Also succeeded, but the first one will report.
% 8.39/2.15 % (2733875)Also succeeded, but the first one will report.
% 8.39/2.15 % (2733889)Refutation found. Thanks to Tanya!
% 8.39/2.15 % SZS status Unsatisfiable for theBenchmark
% 8.39/2.15 % SZS output start Proof for theBenchmark
% See solution above
% 8.39/2.15 % (2733889)------------------------------
% 8.39/2.15 % (2733889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.15 % (2733889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.15 % (2733889)CaDiCaL version: 2.1.3
% 8.39/2.15 % (2733889)Termination reason: Refutation
% 8.39/2.15 % (2733889)Time elapsed: 0.595 s
% 8.39/2.15 % (2733889)Peak memory usage: 132 MB
% 8.39/2.15 % (2733889)Instructions burned: 1220 (million)
% 8.39/2.15 % (2733889)------------------------------
% 8.39/2.15 % (2733889)------------------------------
% 8.39/2.15 % (2733870)Success in time 1.101 s
% 8.39/2.15 % Vampire exiting
%------------------------------------------------------------------------------