%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP181-3 : 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 : n018.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 8.36s 1.93s
% Output : Refutation 8.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 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 : 5 ( 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 : 38 ( 38 !; 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(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(f17,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_1) ).
fof(f18,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_4) ).
fof(f21,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p12x) ).
fof(f22,plain,
least_upper_bound(a,c) = least_upper_bound(c,b),
inference(forward_demodulation,[],[f18,f6]) ).
fof(f23,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(c,b),
inference(forward_demodulation,[],[f17,f5]) ).
fof(f24,plain,
least_upper_bound(c,b) = least_upper_bound(c,a),
inference(forward_demodulation,[],[f22,f6]) ).
fof(f25,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,a),
inference(forward_demodulation,[],[f23,f5]) ).
fof(f73,plain,
! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)),
inference(superposition,[],[f16,f3]) ).
fof(f74,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f75,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f74,f1]) ).
fof(f81,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f75,f75]) ).
fof(f122,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f14,f3]) ).
fof(f195,plain,
! [X0,X1] : multiply(inverse(greatest_lower_bound(inverse(X1),X0)),greatest_lower_bound(identity,multiply(X0,X1))) = X1,
inference(superposition,[],[f75,f73]) ).
fof(f207,plain,
! [X0,X1] : multiply(inverse(inverse(least_upper_bound(X0,X1))),greatest_lower_bound(identity,multiply(inverse(X1),X0))) = X0,
inference(superposition,[],[f195,f20]) ).
fof(f241,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),greatest_lower_bound(identity,multiply(inverse(X1),X0))) = X0,
inference(forward_demodulation,[],[f207,f81]) ).
fof(f534,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),greatest_lower_bound(identity,multiply(inverse(X0),X1))) = X1,
inference(superposition,[],[f241,f6]) ).
fof(f1096,plain,
b = multiply(least_upper_bound(c,a),greatest_lower_bound(identity,multiply(inverse(c),b))),
inference(superposition,[],[f534,f24]) ).
fof(f1111,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),multiply(inverse(X0),greatest_lower_bound(X0,X1))) = X1,
inference(superposition,[],[f534,f122]) ).
fof(f1144,plain,
b = multiply(least_upper_bound(c,a),multiply(inverse(c),greatest_lower_bound(c,b))),
inference(forward_demodulation,[],[f1096,f122]) ).
fof(f1160,plain,
b = multiply(least_upper_bound(c,a),multiply(inverse(c),greatest_lower_bound(c,a))),
inference(forward_demodulation,[],[f1144,f25]) ).
fof(f1164,plain,
a = b,
inference(forward_demodulation,[],[f1160,f1111]) ).
fof(f1168,plain,
$false,
inference(forward_subsumption_resolution,[],[f1164,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:38:23 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 8.36/1.93 % (2080937)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.36/1.93 % (2080947)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=109723894:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.36/1.93 % (2080945)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=11368017:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.36/1.93 % (2080948)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2995420142:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.36/1.93 % (2080943)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=1326940025:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.36/1.93 % (2080944)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1402160401:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.36/1.93 % (2080942)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=4266552705:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.36/1.93 % (2080946)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=407808699:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.36/1.93 % (2080945)Instruction limit reached!
% 8.36/1.93 % (2080945)------------------------------
% 8.36/1.93 % (2080945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.36/1.93 % (2080945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.36/1.93 % (2080945)CaDiCaL version: 2.1.3
% 8.36/1.93 % (2080945)Termination reason: Instruction limit
% 8.36/1.93 % (2080945)Termination phase: Saturation
% 8.36/1.93 % (2080945)Time elapsed: 0.080 s
% 8.36/1.93 % (2080945)Peak memory usage: 88 MB
% 8.36/1.93 % (2080945)Instructions burned: 136 (million)
% 8.36/1.93 % (2080947)Instruction limit reached!
% 8.36/1.93 % (2080947)------------------------------
% 8.36/1.93 % (2080947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.36/1.93 % (2080947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.36/1.93 % (2080947)CaDiCaL version: 2.1.3
% 8.36/1.93 % (2080947)Termination reason: Instruction limit
% 8.36/1.93 % (2080947)Termination phase: Saturation
% 8.36/1.93 % (2080947)Time elapsed: 0.083 s
% 8.36/1.93 % (2080947)Peak memory usage: 90 MB
% 8.36/1.93 % (2080947)Instructions burned: 259 (million)
% 8.36/1.93 % (2080946)Instruction limit reached!
% 8.36/1.93 % (2080946)------------------------------
% 8.36/1.93 % (2080946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.36/1.93 % (2080946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.36/1.93 % (2080946)CaDiCaL version: 2.1.3
% 8.36/1.93 % (2080946)Termination reason: Instruction limit
% 8.36/1.93 % (2080946)Termination phase: Saturation
% 8.36/1.93 % (2080946)Time elapsed: 0.106 s
% 8.36/1.93 % (2080946)Peak memory usage: 89 MB
% 8.36/1.93 % (2080946)Instructions burned: 181 (million)
% 8.36/1.93 % (2080956)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=167212986:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 8.36/1.93 % (2080957)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2118537498:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 8.36/1.93 % (2080958)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3601219116:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 8.36/1.93 % (2080958)Instruction limit reached!
% 8.36/1.93 % (2080958)------------------------------
% 8.36/1.93 % (2080958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.36/1.93 % (2080958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.36/1.93 % (2080958)CaDiCaL version: 2.1.3
% 8.36/1.93 % (2080958)Termination reason: Instruction limit
% 8.36/1.93 % (2080958)Termination phase: Saturation
% 8.36/1.93 % (2080958)Time elapsed: 0.119 s
% 8.36/1.93 % (2080958)Peak memory usage: 92 MB
% 8.36/1.93 % (2080958)Instructions burned: 217 (million)
% 8.36/1.93 % (2080962)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=406522866: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)
% 8.36/1.93 % (2080948)Instruction limit reached!
% 8.36/1.93 % (2080948)------------------------------
% 8.36/1.93 % (2080948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.36/1.93 % (2080948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.36/1.93 % (2080948)CaDiCaL version: 2.1.3
% 8.36/1.93 % (2080948)Termination reason: Instruction limit
% 8.36/1.93 % (2080948)Termination phase: Saturation
% 8.36/1.93 % (2080948)Time elapsed: 0.644 s
% 8.36/1.93 % (2080948)Peak memory usage: 99 MB
% 8.36/1.93 % (2080948)Instructions burned: 1187 (million)
% 8.36/1.93 % (2080943)First to succeed.
% 8.36/1.93 % (2080943)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2080937"
% 8.36/1.93 % (2080962)Instruction limit reached!
% 8.36/1.93 % (2080962)------------------------------
% 8.36/1.93 % (2080962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.36/1.93 % (2080962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.36/1.93 % (2080962)CaDiCaL version: 2.1.3
% 8.36/1.93 % (2080962)Termination reason: Instruction limit
% 8.36/1.93 % (2080962)Termination phase: Saturation
% 8.36/1.93 % (2080962)Time elapsed: 0.180 s
% 8.36/1.93 % (2080962)Peak memory usage: 91 MB
% 8.36/1.93 % (2080962)Instructions burned: 318 (million)
% 8.36/1.93 % (2080942)Also succeeded, but the first one will report.
% 8.36/1.93 % (2080964)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=1166062668:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 8.36/1.93 % (2080965)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=849824240:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 8.36/1.93 % (2080957)Also succeeded, but the first one will report.
% 8.36/1.93 % (2080943)Refutation found. Thanks to Tanya!
% 8.36/1.93 % SZS status Unsatisfiable for theBenchmark
% 8.36/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 8.36/1.93 % (2080943)------------------------------
% 8.36/1.93 % (2080943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.36/1.93 % (2080943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.36/1.93 % (2080943)CaDiCaL version: 2.1.3
% 8.36/1.93 % (2080943)Termination reason: Refutation
% 8.36/1.93 % (2080943)Time elapsed: 0.715 s
% 8.36/1.93 % (2080943)Peak memory usage: 129 MB
% 8.36/1.93 % (2080943)Instructions burned: 1097 (million)
% 8.36/1.93 % (2080943)------------------------------
% 8.36/1.93 % (2080943)------------------------------
% 8.36/1.93 % (2080937)Success in time 1.131 s
% 8.36/1.93 % Vampire exiting
%------------------------------------------------------------------------------