%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 10:16:29 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ equalish(X0,X1)
| ~ product(X2,X3,X0)
| product(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
fof(f8,axiom,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
fof(f9,axiom,
equalish(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_equals_c) ).
fof(f10,negated_conjecture,
~ equalish(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity) ).
fof(f11,plain,
! [X0] : ~ product(identity,X0,X0),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| product(X0,X1,X3)
| product(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( product(X2,X3,X0)
| ~ equalish(X0,X1)
| ~ product(X2,X3,X1) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f18,plain,
! [X0,X1] :
( product(X0,X1,c)
| product(X0,X1,a) ),
inference(resolution,[],[f14,f10]) ).
fof(f20,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| ~ equalish(X0,X1) ),
inference(resolution,[],[f17,f11]) ).
fof(f24,plain,
! [X0] :
( product(identity,X0,a)
| ~ equalish(X0,c) ),
inference(resolution,[],[f20,f18]) ).
fof(f28,plain,
! [X0] :
( ~ equalish(X0,c)
| ~ equalish(X0,a) ),
inference(resolution,[],[f24,f20]) ).
fof(f29,plain,
~ equalish(b,a),
inference(resolution,[],[f28,f9]) ).
fof(f31,plain,
! [X0,X1] :
( product(X0,X1,b)
| product(X0,X1,a) ),
inference(resolution,[],[f29,f14]) ).
fof(f33,plain,
! [X0] :
( product(identity,X0,a)
| ~ equalish(X0,b) ),
inference(resolution,[],[f31,f20]) ).
fof(f35,plain,
~ equalish(a,b),
inference(resolution,[],[f33,f11]) ).
fof(f41,plain,
$false,
inference(resolution,[],[f35,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:16:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.45 % (3237230)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (3237241)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=420832597:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.45 % (3237241) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3237230-3237241"...
% 0.15/0.45 % (3237241)...printing done.
% 0.15/0.45 % (3237241)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.45 % (3237241)------------------------------
% 0.15/0.45 % (3237241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.45 % (3237241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.45 % (3237241)CaDiCaL version: 2.1.3
% 0.15/0.45 % (3237241)Termination reason: Refutation
% 0.15/0.45 % (3237241)Time elapsed: 0.002 s
% 0.15/0.45 % (3237241)Peak memory usage: 11 MB
% 0.15/0.45 % (3237241)Instructions burned: 1 (million)
% 0.15/0.45 % (3237230)Success in time 0.023 s
% 0.15/0.45 % Vampire exiting
%------------------------------------------------------------------------------