%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 10:16:21 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 43 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f9,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
fof(f10,axiom,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
fof(f11,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_equals_d) ).
fof(f12,plain,
d != inverse(c),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[],[f6,f2]) ).
fof(f21,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X3,X0,X1)
| product(X3,X2,identity) ),
inference(resolution,[],[f7,f4]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f7,f1]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,X3)
| ~ product(X0,X1,X2)
| product(X2,inverse(X1),X3) ),
inference(resolution,[],[f8,f4]) ).
fof(f96,plain,
! [X2,X0,X1] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f23,f3]) ).
fof(f122,plain,
! [X0] :
( ~ product(X0,inverse(b),a)
| product(X0,d,identity) ),
inference(resolution,[],[f21,f10]) ).
fof(f138,plain,
! [X2,X0,X1] :
( product(X2,inverse(X1),X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f30,f2]) ).
fof(f356,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| inverse(X0) = X1 ),
inference(resolution,[],[f96,f13]) ).
fof(f470,plain,
! [X0] :
( ~ product(a,b,X0)
| product(X0,d,identity) ),
inference(resolution,[],[f138,f122]) ).
fof(f1477,plain,
product(c,d,identity),
inference(resolution,[],[f470,f9]) ).
fof(f1590,plain,
d = inverse(c),
inference(resolution,[],[f356,f1477]) ).
fof(f1591,plain,
$false,
inference(forward_subsumption_resolution,[],[f1590,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:13:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.16/0.49 % (2823495)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (2823504)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4124005996:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (2823501)% WARNING: option uhcvi not known.
% 0.16/0.49 % (2823503)dis+10_1_sil=32000:sp=arity:random_seed=1346509516:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (2823500)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4107908768_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % (2823502)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4267546185:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (2823501)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=91683224:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (2823506)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1685975481:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % (2823505)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2141584593:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % TRYING [1]
% 0.16/0.49 % TRYING [2]
% 0.16/0.49 % TRYING [3]
% 0.16/0.49 % TRYING [4]
% 0.16/0.49 % TRYING [5]
% 0.16/0.49 % (2823504)Instruction limit reached!
% 0.16/0.49 % (2823504)------------------------------
% 0.16/0.49 % (2823504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (2823504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (2823504)CaDiCaL version: 2.1.3
% 0.16/0.49 % (2823504)Termination reason: Instruction limit
% 0.16/0.49 % (2823504)Termination phase: Saturation
% 0.16/0.49 % (2823504)Time elapsed: 0.036 s
% 0.16/0.49 % (2823504)Peak memory usage: 11 MB
% 0.16/0.49 % (2823504)Instructions burned: 119 (million)
% 0.16/0.49 % TRYING [6]
% 0.16/0.49 % (2823503) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2823495-2823503"...
% 0.16/0.49 % (2823503)...printing done.
% 0.16/0.49 % (2823503)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (2823503)------------------------------
% 0.16/0.49 % (2823503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (2823503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (2823503)CaDiCaL version: 2.1.3
% 0.16/0.49 % (2823503)Termination reason: Refutation
% 0.16/0.49 % (2823503)Time elapsed: 0.038 s
% 0.16/0.49 % (2823503)Peak memory usage: 11 MB
% 0.16/0.49 % (2823503)Instructions burned: 56 (million)
% 0.16/0.49 % (2823495)Success in time 0.07 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------