%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 10:13:17 AM UTC 2026
% Result : Unsatisfiable 2.34s 0.94s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 57 unt; 6 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
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/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f17,axiom,
greatest_lower_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39d_1) ).
fof(f18,plain,
b = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p39d) ).
fof(f20,plain,
inverse(b) != least_upper_bound(inverse(a),inverse(b)),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
! [X0] : sF0(X0) = multiply(identity,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f22,plain,
! [X0] : multiply(identity,X0) = sF0(X0),
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f22]) ).
fof(f24,definition,
! [X0] : sF1(X0) = multiply(inverse(X0),X0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f25,plain,
! [X0] : multiply(inverse(X0),X0) = sF1(X0),
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
! [X0] : identity = sF1(X0),
inference(definition_folding,[],[f3,f25]) ).
fof(f27,definition,
sF2 = greatest_lower_bound(a,b),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
greatest_lower_bound(a,b) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
b = sF2,
inference(definition_folding,[],[f18,f28]) ).
fof(f30,definition,
sF3 = inverse(b),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f31,plain,
inverse(b) = sF3,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF4 = inverse(a),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f33,plain,
inverse(a) = sF4,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF5 = least_upper_bound(sF4,sF3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f35,plain,
least_upper_bound(sF4,sF3) = sF5,
inference(reorient_equations,[],[f34]) ).
fof(f36,plain,
sF3 != sF5,
inference(definition_folding,[],[f20,f35,f31,f33,f31]) ).
fof(f37,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f26,f25]) ).
fof(f38,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f23,f22]) ).
fof(f45,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f38]) ).
fof(f56,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f37]) ).
fof(f57,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f37]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f56,f38]) ).
fof(f126,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f69,f37]) ).
fof(f203,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f69,f126]) ).
fof(f576,plain,
! [X0] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[],[f69,f203]) ).
fof(f577,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f576,f126]) ).
fof(f591,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f126,f577]) ).
fof(f598,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f69,f577]) ).
fof(f1743,plain,
! [X0,X1] : multiply(inverse(X0),X0) = least_upper_bound(identity,multiply(inverse(X0),greatest_lower_bound(X0,X1))),
inference(superposition,[],[f57,f11]) ).
fof(f1818,plain,
! [X0,X1] : identity = least_upper_bound(identity,multiply(inverse(X0),greatest_lower_bound(X0,X1))),
inference(forward_demodulation,[],[f1743,f37]) ).
fof(f3499,plain,
! [X0] : identity = least_upper_bound(identity,multiply(sF4,greatest_lower_bound(a,X0))),
inference(superposition,[],[f1818,f33]) ).
fof(f3727,plain,
identity = least_upper_bound(identity,multiply(sF4,sF2)),
inference(superposition,[],[f3499,f28]) ).
fof(f3758,plain,
identity = least_upper_bound(identity,multiply(sF4,b)),
inference(forward_demodulation,[],[f3727,f29]) ).
fof(f3768,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(multiply(sF4,b),X0)),
inference(superposition,[],[f45,f3758]) ).
fof(f3773,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(sF4,multiply(b,X0))),
inference(forward_demodulation,[],[f3768,f4]) ).
fof(f3778,plain,
! [X0] : least_upper_bound(X0,multiply(sF4,multiply(b,X0))) = X0,
inference(forward_demodulation,[],[f3773,f38]) ).
fof(f4038,plain,
! [X0] : multiply(inverse(b),X0) = least_upper_bound(multiply(inverse(b),X0),multiply(sF4,X0)),
inference(superposition,[],[f3778,f598]) ).
fof(f4075,plain,
! [X0] : multiply(inverse(b),X0) = least_upper_bound(multiply(sF4,X0),multiply(inverse(b),X0)),
inference(forward_demodulation,[],[f4038,f6]) ).
fof(f4083,plain,
! [X0] : multiply(inverse(b),X0) = multiply(least_upper_bound(sF4,inverse(b)),X0),
inference(forward_demodulation,[],[f4075,f15]) ).
fof(f4087,plain,
! [X0] : multiply(sF3,X0) = multiply(least_upper_bound(sF4,sF3),X0),
inference(forward_demodulation,[],[f4083,f31]) ).
fof(f4089,plain,
! [X0] : multiply(sF3,X0) = multiply(sF5,X0),
inference(forward_demodulation,[],[f4087,f35]) ).
fof(f4122,plain,
sF5 = multiply(sF3,identity),
inference(superposition,[],[f591,f4089]) ).
fof(f4125,plain,
sF3 = sF5,
inference(forward_demodulation,[],[f4122,f591]) ).
fof(f4145,plain,
sF3 != sF3,
inference(superposition,[],[f36,f4125]) ).
fof(f4157,plain,
$false,
inference(trivial_inequality_removal,[],[f4145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 09:36:50 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.33 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
% 2.34/0.93 % (2117904)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.34/0.93 % (2117986)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2607975958:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.34/0.93 % (2117987)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=839284695:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.34/0.93 % (2117990)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=193234830:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.34/0.93 % (2117992)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2944113000:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.34/0.93 % (2117985)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=1869338697:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.34/0.94 % (2117984)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=2583008496:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.34/0.94 % (2117989)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1045597364:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.34/0.94 % (2117989)First to succeed.
% 2.34/0.94 % (2117989)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2117904"
% 2.34/0.94 % (2117987)Instruction limit reached!
% 2.34/0.94 % (2117987)------------------------------
% 2.34/0.94 % (2117987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.94 % (2117987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.94 % (2117987)CaDiCaL version: 2.1.3
% 2.34/0.94 % (2117987)Termination reason: Instruction limit
% 2.34/0.94 % (2117987)Termination phase: Saturation
% 2.34/0.94 % (2117987)Time elapsed: 0.046 s
% 2.34/0.94 % (2117987)Peak memory usage: 89 MB
% 2.34/0.94 % (2117987)Instructions burned: 138 (million)
% 2.34/0.94 % (2117990)Instruction limit reached!
% 2.34/0.94 % (2117990)------------------------------
% 2.34/0.94 % (2117990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.94 % (2117990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.94 % (2117990)CaDiCaL version: 2.1.3
% 2.34/0.94 % (2117990)Termination reason: Instruction limit
% 2.34/0.94 % (2117990)Termination phase: Saturation
% 2.34/0.94 % (2117990)Time elapsed: 0.088 s
% 2.34/0.94 % (2117990)Peak memory usage: 91 MB
% 2.34/0.94 % (2117990)Instructions burned: 257 (million)
% 2.34/0.94 % (2118036)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1895882819:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 2.34/0.94 % (2118037)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3836172937:i=4948:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/4948Mi)
% 2.34/0.94 % (2117989)Refutation found. Thanks to Tanya!
% 2.34/0.94 % SZS status Unsatisfiable for theBenchmark
% 2.34/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 2.34/0.94 % (2117989)------------------------------
% 2.34/0.94 % (2117989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.94 % (2117989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.94 % (2117989)CaDiCaL version: 2.1.3
% 2.34/0.94 % (2117989)Termination reason: Refutation
% 2.34/0.94 % (2117989)Time elapsed: 0.044 s
% 2.34/0.94 % (2117989)Peak memory usage: 90 MB
% 2.34/0.94 % (2117989)Instructions burned: 136 (million)
% 2.34/0.94 % (2117989)------------------------------
% 2.34/0.94 % (2117989)------------------------------
% 2.34/0.94 % (2117904)Success in time 0.311 s
% 2.34/0.94 % Vampire exiting
%------------------------------------------------------------------------------