%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP166-3 : 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 : n001.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 10:17:00 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
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(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
fof(f19,axiom,
least_upper_bound(b,identity) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat3a_2) ).
fof(f20,plain,
b = least_upper_bound(b,identity),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat3a) ).
fof(f22,plain,
multiply(b,a) != least_upper_bound(a,multiply(b,a)),
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
b = least_upper_bound(identity,b),
inference(superposition,[],[f6,f20]) ).
fof(f119,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f1]) ).
fof(f971,plain,
multiply(b,a) != multiply(least_upper_bound(identity,b),a),
inference(superposition,[],[f22,f119]) ).
fof(f972,plain,
multiply(b,a) != multiply(b,a),
inference(forward_demodulation,[],[f971,f23]) ).
fof(f973,plain,
$false,
inference(trivial_inequality_removal,[],[f972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:40:31 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.16/0.47 % (3298866)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3298872)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3298872)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2543825630:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3298871)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2060258784_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3298873)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2071622050:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3298876)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=56356213:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (3298874)dis+10_1_sil=32000:sp=arity:random_seed=1586316096:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3298875)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=513752742:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3298877)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=839714515:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (3298872) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3298866-3298872"...
% 0.16/0.47 % (3298872)...printing done.
% 0.16/0.47 % (3298872)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3298872)------------------------------
% 0.16/0.47 % (3298872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3298872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3298872)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3298872)Termination reason: Refutation
% 0.16/0.47 % (3298872)Time elapsed: 0.013 s
% 0.16/0.47 % (3298872)Peak memory usage: 11 MB
% 0.16/0.47 % (3298872)Instructions burned: 39 (million)
% 0.16/0.47 % (3298866)Success in time 0.046 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------