%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP175-4 : 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 : n026.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 10:13:11 AM UTC 2026
% Result : Unsatisfiable 2.90s 1.38s
% Output : Refutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
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(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p06d_1) ).
fof(f18,plain,
identity = greatest_lower_bound(identity,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p06d) ).
fof(f20,plain,
multiply(inverse(a),multiply(b,a)) != least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),
inference(reorient_equations,[],[f19]) ).
fof(f23,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f30,plain,
b = least_upper_bound(b,identity),
inference(superposition,[],[f23,f18]) ).
fof(f37,plain,
b = least_upper_bound(identity,b),
inference(forward_demodulation,[],[f30,f6]) ).
fof(f298,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f3]) ).
fof(f610,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f1]) ).
fof(f6549,plain,
multiply(inverse(a),multiply(b,a)) != multiply(inverse(a),least_upper_bound(a,multiply(b,a))),
inference(superposition,[],[f20,f298]) ).
fof(f6584,plain,
multiply(inverse(a),multiply(b,a)) != multiply(inverse(a),multiply(least_upper_bound(identity,b),a)),
inference(forward_demodulation,[],[f6549,f610]) ).
fof(f6617,plain,
multiply(inverse(a),multiply(b,a)) != multiply(inverse(a),multiply(b,a)),
inference(forward_demodulation,[],[f6584,f37]) ).
fof(f6618,plain,
$false,
inference(trivial_inequality_removal,[],[f6617]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP175-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.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 09:38:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.90/1.38 % (2578825)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.90/1.38 % (2578836)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3390995163:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.90/1.38 % (2578835)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2997217466:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.90/1.38 % (2578832)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2147080417:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.90/1.38 % (2578831)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=2651853153:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.90/1.38 % (2578833)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2871625372:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.90/1.38 % (2578834)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4013300095:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.90/1.38 % (2578830)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=2749077942:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.90/1.38 % (2578836)First to succeed.
% 2.90/1.38 % (2578836)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2578825"
% 2.90/1.38 % (2578834)Also succeeded, but the first one will report.
% 2.90/1.38 % (2578833)Instruction limit reached!
% 2.90/1.38 % (2578833)------------------------------
% 2.90/1.38 % (2578833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.38 % (2578833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.38 % (2578833)CaDiCaL version: 2.1.3
% 2.90/1.38 % (2578833)Termination reason: Instruction limit
% 2.90/1.38 % (2578833)Termination phase: Saturation
% 2.90/1.38 % (2578833)Time elapsed: 0.082 s
% 2.90/1.38 % (2578833)Peak memory usage: 89 MB
% 2.90/1.38 % (2578833)Instructions burned: 137 (million)
% 2.90/1.38 % (2578835)Instruction limit reached!
% 2.90/1.38 % (2578835)------------------------------
% 2.90/1.38 % (2578835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.38 % (2578835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.38 % (2578835)CaDiCaL version: 2.1.3
% 2.90/1.38 % (2578835)Termination reason: Instruction limit
% 2.90/1.38 % (2578835)Termination phase: Saturation
% 2.90/1.38 % (2578835)Time elapsed: 0.170 s
% 2.90/1.38 % (2578835)Peak memory usage: 91 MB
% 2.90/1.38 % (2578835)Instructions burned: 258 (million)
% 2.90/1.38 % (2578836)Refutation found. Thanks to Tanya!
% 2.90/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.90/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.90/1.38 % (2578836)------------------------------
% 2.90/1.38 % (2578836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.38 % (2578836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.38 % (2578836)CaDiCaL version: 2.1.3
% 2.90/1.38 % (2578836)Termination reason: Refutation
% 2.90/1.38 % (2578836)Time elapsed: 0.061 s
% 2.90/1.38 % (2578836)Peak memory usage: 90 MB
% 2.90/1.38 % (2578836)Instructions burned: 200 (million)
% 2.90/1.38 % (2578836)------------------------------
% 2.90/1.38 % (2578836)------------------------------
% 2.90/1.38 % (2578825)Success in time 0.329 s
% 2.90/1.38 % Vampire exiting
%------------------------------------------------------------------------------