%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP029-2 : 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 : n002.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 10:16:26 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f14,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f15,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f16,negated_conjecture,
! [X0] : ~ product(not_right_identity(X0),X0,not_right_identity(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(identity,X1,X3)
| product(inverse(X0),X2,X3) ),
inference(resolution,[],[f12,f15]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(identity,X2,X3)
| product(X0,X1,X3) ),
inference(resolution,[],[f13,f14]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ product(inverse(X0),X2,X3)
| ~ product(X0,X1,X2)
| product(identity,X1,X3) ),
inference(resolution,[],[f13,f15]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ product(identity,multiply(X0,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[],[f41,f10]) ).
fof(f96,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| product(inverse(inverse(X0)),identity,X1) ),
inference(resolution,[],[f31,f15]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ product(identity,X0,X1)
| product(inverse(X2),multiply(X2,X0),X1) ),
inference(resolution,[],[f31,f10]) ).
fof(f194,plain,
! [X0] : product(inverse(inverse(X0)),identity,X0),
inference(resolution,[],[f96,f14]) ).
fof(f228,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[],[f97,f14]) ).
fof(f233,plain,
! [X0,X1] :
( ~ product(inverse(X0),X1,identity)
| product(identity,X1,X0) ),
inference(resolution,[],[f194,f42]) ).
fof(f2713,plain,
! [X0] : product(identity,multiply(X0,identity),X0),
inference(resolution,[],[f233,f228]) ).
fof(f2721,plain,
! [X0] : product(X0,identity,X0),
inference(resolution,[],[f2713,f86]) ).
fof(f2791,plain,
$false,
inference(resolution,[],[f2721,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP029-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n002.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 09:18:06 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.17/0.51 % (3264713)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (3264734)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=778948901:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % (3264730)% WARNING: option uhcvi not known.
% 0.17/0.51 % (3264729)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=42976315_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % (3264732)dis+10_1_sil=32000:sp=arity:random_seed=1505321607:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (3264730)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=323200146:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (3264731)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=716737912:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (3264733)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1614964554:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % (3264735)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1406908771:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % TRYING [1]
% 0.17/0.51 % TRYING [2]
% 0.17/0.51 % TRYING [3]
% 0.17/0.51 % TRYING [4]
% 0.17/0.51 % TRYING [5]
% 0.17/0.51 % (3264734) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3264713-3264734"...
% 0.17/0.51 % (3264734)...printing done.
% 0.17/0.51 % (3264734)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (3264734)------------------------------
% 0.17/0.51 % (3264734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (3264734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (3264734)CaDiCaL version: 2.1.3
% 0.17/0.51 % (3264734)Termination reason: Refutation
% 0.17/0.51 % (3264734)Time elapsed: 0.031 s
% 0.17/0.51 % (3264734)Peak memory usage: 12 MB
% 0.17/0.51 % (3264734)Instructions burned: 82 (million)
% 0.17/0.51 % (3264713)Success in time 0.068 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------