%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP001+6 : 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 10:16:19 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 173 ( 50 ~; 42 |; 66 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 207 ( 189 !; 18 ?)
% 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) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity) ).
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) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
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] : product(X20,X20,X0)
=> ! [X21,X22,X23] :
( product(X21,X22,X23)
=> product(X22,X21,X23) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ? [X21,X22,X23] :
( ~ product(X22,X21,X23)
& product(X21,X22,X23) )
& ! [X20] : product(X20,X20,X0)
& ! [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] :
( ? [X21,X22,X23] :
( ~ product(X22,X21,X23)
& product(X21,X22,X23) )
& ! [X20] : product(X20,X20,X0)
& ! [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,
? [X0] :
( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
& ! [X4] : product(X4,X4,X0)
& ! [X5,X6] :
? [X7] : product(X5,X6,X7)
& ! [X8,X9,X10,X11,X12,X13] :
( product(X8,X12,X13)
| ~ product(X8,X9,X11)
| ~ product(X9,X10,X12)
| ~ product(X11,X10,X13) )
& ! [X14,X15,X16,X17,X18,X19] :
( product(X17,X16,X19)
| ~ product(X14,X15,X17)
| ~ product(X15,X16,X18)
| ~ product(X14,X18,X19) )
& ! [X20] : product(X20,X0,X20)
& ! [X21] : product(X0,X21,X21)
& ! [X22] : product(X22,inverse(X22),X0)
& ! [X23] : product(inverse(X23),X23,X0) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ~ product(sK2,sK1,sK3)
& product(sK1,sK2,sK3)
& ! [X4] : product(X4,X4,sK0)
& ! [X5,X6] : product(X5,X6,sK4(X5,X6))
& ! [X8,X9,X10,X11,X12,X13] :
( product(X8,X12,X13)
| ~ product(X8,X9,X11)
| ~ product(X9,X10,X12)
| ~ product(X11,X10,X13) )
& ! [X14,X15,X16,X17,X18,X19] :
( product(X17,X16,X19)
| ~ product(X14,X15,X17)
| ~ product(X15,X16,X18)
| ~ product(X14,X18,X19) )
& ! [X20] : product(X20,sK0,X20)
& ! [X21] : product(sK0,X21,X21)
& ! [X22] : product(X22,inverse(X22),sK0)
& ! [X23] : product(inverse(X23),X23,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4(X5,X6))],[f6]) ).
fof(f10,plain,
! [X21] : product(sK0,X21,X21),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X20] : product(X20,sK0,X20),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X18,X19,X16,X14,X17,X15] :
( product(X17,X16,X19)
| ~ product(X14,X15,X17)
| ~ product(X15,X16,X18)
| ~ product(X14,X18,X19) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X10,X11,X8,X9,X12,X13] :
( product(X8,X12,X13)
| ~ product(X8,X9,X11)
| ~ product(X9,X10,X12)
| ~ product(X11,X10,X13) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X4] : product(X4,X4,sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
product(sK1,sK2,sK3),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
~ product(sK2,sK1,sK3),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
product(sK2,sK1,sK3),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f19,plain,
~ product(sK1,sK2,sK3),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f20,plain,
! [X4] : ~ product(X4,X4,sK0),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f22,plain,
! [X10,X11,X8,X9,X12,X13] :
( product(X11,X10,X13)
| product(X8,X9,X11)
| product(X9,X10,X12)
| ~ product(X8,X12,X13) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f23,plain,
! [X18,X19,X16,X14,X17,X15] :
( product(X15,X16,X18)
| product(X14,X15,X17)
| ~ product(X17,X16,X19)
| product(X14,X18,X19) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f24,plain,
! [X20] : ~ product(X20,sK0,X20),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f25,plain,
! [X21] : ~ product(sK0,X21,X21),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( product(X0,X1,sK0)
| product(X1,X2,X3)
| ~ product(X0,X3,X2) ),
inference(resolution,[],[f22,f25]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( product(X0,sK0,X3)
| ~ product(X2,X1,X3)
| product(X0,X1,X2) ),
inference(resolution,[],[f23,f20]) ).
fof(f156,plain,
! [X2,X0,X1] :
( product(X0,X1,X2)
| ~ product(X0,X2,X1) ),
inference(resolution,[],[f33,f20]) ).
fof(f216,plain,
~ product(sK1,sK3,sK2),
inference(resolution,[],[f156,f19]) ).
fof(f433,plain,
! [X2,X0,X1] :
( product(X2,X1,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[],[f63,f24]) ).
fof(f567,plain,
~ product(sK2,sK3,sK1),
inference(resolution,[],[f433,f216]) ).
fof(f583,plain,
~ product(sK2,sK1,sK3),
inference(resolution,[],[f567,f156]) ).
fof(f593,plain,
$false,
inference(resolution,[],[f583,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001+6 : 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 09:12:45 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.17/0.48 % (2132567)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (2132575)dis+10_1_sil=32000:sp=arity:random_seed=2944958724:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (2132573)% WARNING: option uhcvi not known.
% 0.17/0.48 % (2132576)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1822458230:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (2132573)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2268324807:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (2132572)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=238917391_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (2132574)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=13078875:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (2132577)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2130322821:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % (2132578)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2278647010:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % (2132578) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2132567-2132578"...
% 0.17/0.48 % (2132578)...printing done.
% 0.17/0.48 % (2132578)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (2132578)------------------------------
% 0.17/0.48 % (2132578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2132578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2132578)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2132578)Termination reason: Refutation
% 0.17/0.48 % (2132578)Time elapsed: 0.013 s
% 0.17/0.48 % (2132578)Peak memory usage: 12 MB
% 0.17/0.48 % (2132578)Instructions burned: 19 (million)
% 0.17/0.48 % (2132567)Success in time 0.06 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------