%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 10:16:22 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 134 ( 38 ~; 33 |; 51 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 167 ( 152 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X2,X4)
& product(X2,X3,X5)
& product(X4,X3,X6) )
=> product(X1,X5,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X2,X4)
& product(X2,X3,X5)
& product(X1,X5,X6) )
=> product(X4,X3,X6) )
& ! [X1] : product(X1,X0,X1)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(inverse(X1),X1,X0) )
=> ! [X4,X5,X6,X1] :
( ( product(inverse(X4),inverse(X5),X6)
& product(X5,X4,X1) )
=> product(inverse(X6),inverse(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distribution) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X2,X4)
& product(X2,X3,X5)
& product(X4,X3,X6) )
=> product(X1,X5,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X2,X4)
& product(X2,X3,X5)
& product(X1,X5,X6) )
=> product(X4,X3,X6) )
& ! [X1] : product(X1,X0,X1)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(inverse(X1),X1,X0) )
=> ! [X4,X5,X6,X1] :
( ( product(inverse(X4),inverse(X5),X6)
& product(X5,X4,X1) )
=> product(inverse(X6),inverse(X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ! [X0] :
( ( ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ! [X4,X5,X6,X7,X8,X9] :
( ( product(X4,X5,X7)
& product(X5,X6,X8)
& product(X7,X6,X9) )
=> product(X4,X8,X9) )
& ! [X10,X11,X12,X13,X14,X15] :
( ( product(X10,X11,X13)
& product(X11,X12,X14)
& product(X10,X14,X15) )
=> product(X13,X12,X15) )
& ! [X16] : product(X16,X0,X16)
& ! [X17] : product(X0,X17,X17)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X19] : product(inverse(X19),X19,X0) )
=> ! [X20,X21,X22,X23] :
( ( product(inverse(X20),inverse(X21),X22)
& product(X21,X20,X23) )
=> product(inverse(X22),inverse(X23),X0) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ? [X20,X21,X22,X23] :
( ~ product(inverse(X22),inverse(X23),X0)
& product(inverse(X20),inverse(X21),X22)
& product(X21,X20,X23) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ! [X4,X5,X6,X7,X8,X9] :
( product(X4,X8,X9)
| ~ product(X4,X5,X7)
| ~ product(X5,X6,X8)
| ~ product(X7,X6,X9) )
& ! [X10,X11,X12,X13,X14,X15] :
( product(X13,X12,X15)
| ~ product(X10,X11,X13)
| ~ product(X11,X12,X14)
| ~ product(X10,X14,X15) )
& ! [X16] : product(X16,X0,X16)
& ! [X17] : product(X0,X17,X17)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X19] : product(inverse(X19),X19,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
( ? [X20,X21,X22,X23] :
( ~ product(inverse(X22),inverse(X23),X0)
& product(inverse(X20),inverse(X21),X22)
& product(X21,X20,X23) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3)
& ! [X4,X5,X6,X7,X8,X9] :
( product(X4,X8,X9)
| ~ product(X4,X5,X7)
| ~ product(X5,X6,X8)
| ~ product(X7,X6,X9) )
& ! [X10,X11,X12,X13,X14,X15] :
( product(X13,X12,X15)
| ~ product(X10,X11,X13)
| ~ product(X11,X12,X14)
| ~ product(X10,X14,X15) )
& ! [X16] : product(X16,X0,X16)
& ! [X17] : product(X0,X17,X17)
& ! [X18] : product(X18,inverse(X18),X0)
& ! [X19] : product(inverse(X19),X19,X0) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
product(sK2,sK1,sK4),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
product(inverse(sK1),inverse(sK2),sK3),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
~ product(inverse(sK3),inverse(sK4),sK0),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X8,X6,X9,X7,X4,X5] :
( ~ product(X7,X6,X9)
| ~ product(X5,X6,X8)
| ~ product(X4,X5,X7)
| product(X4,X8,X9) ),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
! [X10,X11,X14,X15,X12,X13] :
( ~ product(X11,X12,X14)
| ~ product(X10,X14,X15)
| ~ product(X10,X11,X13)
| product(X13,X12,X15) ),
inference(cnf_transformation,[],[f5]) ).
fof(f11,plain,
! [X19] : product(inverse(X19),X19,sK0),
inference(cnf_transformation,[],[f5]) ).
fof(f12,plain,
! [X18] : product(X18,inverse(X18),sK0),
inference(cnf_transformation,[],[f5]) ).
fof(f13,plain,
! [X17] : product(sK0,X17,X17),
inference(cnf_transformation,[],[f5]) ).
fof(f14,plain,
! [X16] : product(X16,sK0,X16),
inference(cnf_transformation,[],[f5]) ).
fof(f16,plain,
! [X2,X3,X0,X1] :
( ~ product(X2,X0,X3)
| ~ product(X0,sK0,X1)
| product(X2,X1,X3) ),
inference(resolution,[],[f9,f14]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X3,X0,X1)
| product(X3,X2,sK0) ),
inference(resolution,[],[f9,f12]) ).
fof(f19,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,inverse(X1))
| ~ product(X0,X1,X2)
| product(X3,X2,sK0) ),
inference(resolution,[],[f9,f11]) ).
fof(f21,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,sK0)
| ~ product(X0,X1,X2)
| product(X3,X2,X1) ),
inference(resolution,[],[f9,f13]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,sK0,X1)
| ~ product(X0,X2,X3)
| product(X3,inverse(X2),X1) ),
inference(resolution,[],[f10,f12]) ).
fof(f35,plain,
! [X0,X1] :
( ~ product(X0,sK0,X1)
| product(sK0,X1,X0) ),
inference(resolution,[],[f16,f13]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(inverse(X0),X2,X1) ),
inference(resolution,[],[f21,f11]) ).
fof(f59,plain,
! [X0] :
( ~ product(X0,inverse(sK1),sK2)
| product(X0,sK3,sK0) ),
inference(resolution,[],[f17,f7]) ).
fof(f62,plain,
! [X0,X1] :
( ~ product(sK0,X0,X1)
| product(inverse(X0),X1,sK0) ),
inference(resolution,[],[f19,f14]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X2,inverse(X1),X0) ),
inference(resolution,[],[f24,f14]) ).
fof(f322,plain,
product(sK4,inverse(sK1),sK2),
inference(resolution,[],[f67,f6]) ).
fof(f332,plain,
product(sK4,sK3,sK0),
inference(resolution,[],[f322,f59]) ).
fof(f350,plain,
product(inverse(sK4),sK0,sK3),
inference(resolution,[],[f332,f39]) ).
fof(f397,plain,
product(sK0,sK3,inverse(sK4)),
inference(resolution,[],[f350,f35]) ).
fof(f442,plain,
product(inverse(sK3),inverse(sK4),sK0),
inference(resolution,[],[f397,f62]) ).
fof(f455,plain,
$false,
inference(forward_subsumption_resolution,[],[f442,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n011.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 09:13:45 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.17/0.47 % (2135490)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2135495)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=454491447_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (2135496)% WARNING: option uhcvi not known.
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (2135496)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=883820712:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2135497)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1823483859:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2135498)dis+10_1_sil=32000:sp=arity:random_seed=3177623351:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2135499)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2189283015:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2135501)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1786264710:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (2135500)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=82251091:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2135496) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2135490-2135496"...
% 0.17/0.47 % (2135496)...printing done.
% 0.17/0.47 % (2135496)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (2135496)------------------------------
% 0.17/0.47 % (2135496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (2135496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (2135496)CaDiCaL version: 2.1.3
% 0.17/0.47 % (2135496)Termination reason: Refutation
% 0.17/0.47 % (2135496)Time elapsed: 0.011 s
% 0.17/0.47 % (2135496)Peak memory usage: 11 MB
% 0.17/0.47 % (2135496)Instructions burned: 15 (million)
% 0.17/0.47 % (2135490)Success in time 0.047 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------