%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 10:17:07 AM UTC 2026
% Result : Unsatisfiable 0.30s 0.63s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',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/Axioms/GRP004-2.ax',monotony_lub1) ).
fof(f17,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p23x) ).
fof(f19,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f20,plain,
! [X0] : multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(a,b),multiply(inverse(X0),X0)),
inference(superposition,[],[f17,f3]) ).
fof(f21,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f19,f4]) ).
fof(f26,plain,
! [X0] : multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(inverse(X0),X0),multiply(a,b)),
inference(superposition,[],[f20,f6]) ).
fof(f83,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f21,f3]) ).
fof(f85,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f21,f21]) ).
fof(f88,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f83,f85]) ).
fof(f111,plain,
! [X0,X1] : multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(superposition,[],[f88,f3]) ).
fof(f307,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f21,f111]) ).
fof(f400,plain,
! [X0] : multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(X0,inverse(X0)),multiply(a,b)),
inference(superposition,[],[f26,f307]) ).
fof(f492,plain,
multiply(a,least_upper_bound(inverse(a),b)) != multiply(a,least_upper_bound(inverse(a),b)),
inference(superposition,[],[f400,f13]) ).
fof(f495,plain,
$false,
inference(trivial_inequality_removal,[],[f492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.20/0.48 % Computer : n016.cluster.edu
% 0.20/0.48 % Model : x86_64 x86_64
% 0.20/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.48 % Memory : 8046.5625MB
% 0.20/0.48 % OS : Linux 6.8.0-71-generic
% 0.20/0.48 % CPULimit : 300
% 0.20/0.48 % WCLimit : 300
% 0.20/0.48 % DateTime : Sun Sep 27 09:41:47 UTC 2026
% 0.20/0.49 % CPUTime :
% 0.20/0.49 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.54 Running first-order model finding
% 0.26/0.54 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.63 % (2373447)Will run a generic schedule for satisfiability detection.
% 0.30/0.63 % (2373452)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2483875236_2999 on theBenchmark for (2999ds/0Mi)
% 0.30/0.63 % TRYING [1]
% 0.30/0.63 % TRYING [2]
% 0.30/0.63 % TRYING [3]
% 0.30/0.63 % (2373453)% WARNING: option uhcvi not known.
% 0.30/0.63 % TRYING [4]
% 0.30/0.63 % (2373456)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1678897552:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.30/0.63 % (2373453)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3737441215:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.30/0.63 % (2373455)dis+10_1_sil=32000:sp=arity:random_seed=3958803834:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.30/0.63 % (2373454)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=531635440:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.30/0.63 % (2373458)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2289570680:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.30/0.63 % (2373457)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3408990299:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.30/0.63 % (2373457) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2373447-2373457"...
% 0.30/0.63 % TRYING [5]
% 0.30/0.63 % (2373457)...printing done.
% 0.30/0.63 % (2373457)Refutation found. Thanks to Tanya!
% 0.30/0.63 % SZS status Unsatisfiable for theBenchmark
% 0.30/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.63 % (2373457)------------------------------
% 0.30/0.63 % (2373457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.63 % (2373457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.63 % (2373457)CaDiCaL version: 2.1.3
% 0.30/0.63 % (2373457)Termination reason: Refutation
% 0.30/0.63 % (2373457)Time elapsed: 0.023 s
% 0.30/0.63 % (2373457)Peak memory usage: 11 MB
% 0.30/0.63 % (2373457)Instructions burned: 19 (million)
% 0.30/0.63 % (2373447)Success in time 0.072 s
% 0.30/0.63 % Vampire exiting
%------------------------------------------------------------------------------