%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 10:12:07 AM UTC 2026
% Result : Theorem 0.17s 1.70s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 151 ( 40 ~; 30 |; 69 &)
% ( 0 <=>; 12 =>; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 177 ( 156 !; 21 ?)
% 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/sandbox2/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,
? [X0] :
( ? [X1,X2,X3,X4] :
( ~ product(inverse(X3),inverse(X4),X0)
& product(inverse(X1),inverse(X2),X3)
& product(X2,X1,X4) )
& ! [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(inverse(sK3),inverse(sK4),sK0)
& product(inverse(sK1),inverse(sK2),sK3)
& product(sK2,sK1,sK4)
& ! [X5,X6] : product(X5,X6,sK5(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,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X7,sK5(X5,X6))],[f6]) ).
fof(f8,plain,
! [X23] : product(inverse(X23),X23,sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X22] : product(X22,inverse(X22),sK0),
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(X15,X16,X18)
| ~ product(X14,X15,X17)
| product(X17,X16,X19)
| ~ product(X14,X18,X19) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X10,X11,X8,X9,X12,X13] :
( ~ product(X11,X10,X13)
| ~ product(X8,X9,X11)
| ~ product(X9,X10,X12)
| product(X8,X12,X13) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
product(sK2,sK1,sK4),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
product(inverse(sK1),inverse(sK2),sK3),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
~ product(inverse(sK3),inverse(sK4),sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
~ product(sK0,inverse(sK4),sK3),
inference(unit_resulting_resolution,[],[f12,f8,f17,f11]) ).
fof(f85,plain,
product(sK3,sK2,inverse(sK1)),
inference(unit_resulting_resolution,[],[f12,f11,f16,f8]) ).
fof(f295,plain,
~ product(sK3,sK4,sK0),
inference(unit_resulting_resolution,[],[f12,f11,f9,f21]) ).
fof(f328,plain,
~ product(sK3,sK2,inverse(sK1)),
inference(unit_resulting_resolution,[],[f13,f8,f15,f295]) ).
fof(f357,plain,
$false,
inference(forward_subsumption_resolution,[],[f328,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n010.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 09:14:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.08/1.70 % (676576)Detected formulas, will run a generic FOF schedule.
% 5.08/1.70 % (676583)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1405628634:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.08/1.70 % (676581)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2327821986:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.08/1.70 % (676585)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3050340497:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.08/1.70 % (676584)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2467529679:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.08/1.70 % (676582)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2440681583:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.08/1.70 % (676586)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1075484923:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.08/1.70 % (676587)dis-21_1_sil=8000:lcm=predicate:random_seed=1544896698:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.08/1.70 % (676585)Instruction limit reached!
% 5.08/1.70 % (676585)------------------------------
% 5.08/1.70 % (676585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.08/1.70 % (676585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.08/1.70 % (676585)CaDiCaL version: 2.1.3
% 5.08/1.70 % (676585)Termination reason: Instruction limit
% 5.08/1.70 % (676585)Termination phase: Saturation
% 5.08/1.70 % (676585)Time elapsed: 0.069 s
% 5.08/1.70 % (676585)Peak memory usage: 87 MB
% 5.08/1.70 % (676585)Instructions burned: 119 (million)
% 5.08/1.70 % (676584)Instruction limit reached!
% 5.08/1.70 % (676584)------------------------------
% 5.08/1.70 % (676584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.70 % (676584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.70 % (676584)CaDiCaL version: 2.1.3
% 0.17/1.70 % (676584)Termination reason: Instruction limit
% 0.17/1.70 % (676584)Termination phase: Saturation
% 0.17/1.70 % (676584)Time elapsed: 0.070 s
% 0.17/1.70 % (676584)Peak memory usage: 89 MB
% 0.17/1.70 % (676584)Instructions burned: 110 (million)
% 0.17/1.70 % (676586)Instruction limit reached!
% 0.17/1.70 % (676586)------------------------------
% 0.17/1.70 % (676586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.70 % (676586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.70 % (676586)CaDiCaL version: 2.1.3
% 0.17/1.70 % (676586)Termination reason: Instruction limit
% 0.17/1.70 % (676586)Termination phase: Saturation
% 0.17/1.70 % (676586)Time elapsed: 0.084 s
% 0.17/1.70 % (676586)Peak memory usage: 88 MB
% 0.17/1.70 % (676586)Instructions burned: 139 (million)
% 0.17/1.70 % (676587)Instruction limit reached!
% 0.17/1.70 % (676587)------------------------------
% 0.17/1.70 % (676587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.70 % (676587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.70 % (676587)CaDiCaL version: 2.1.3
% 0.17/1.70 % (676587)Termination reason: Instruction limit
% 0.17/1.70 % (676587)Termination phase: Saturation
% 0.17/1.70 % (676587)Time elapsed: 0.073 s
% 0.17/1.70 % (676587)Peak memory usage: 88 MB
% 0.17/1.70 % (676587)Instructions burned: 130 (million)
% 0.17/1.70 % (676596)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4237920815:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.17/1.70 % (676595)lrs+10_1_sil=8000:sp=occurrence:random_seed=3873033785:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.17/1.70 % (676596)First to succeed.
% 0.17/1.70 % (676596)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-676576"
% 0.17/1.70 % (676598)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1047048751:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 0.17/1.70 % (676597)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4268882719:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 0.17/1.70 % (676598)Also succeeded, but the first one will report.
% 0.17/1.70 % (676595)Also succeeded, but the first one will report.
% 0.17/1.70 % (676597)Instruction limit reached!
% 0.17/1.70 % (676597)------------------------------
% 0.17/1.70 % (676597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.70 % (676597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.70 % (676597)CaDiCaL version: 2.1.3
% 0.17/1.70 % (676597)Termination reason: Instruction limit
% 0.17/1.70 % (676597)Termination phase: Saturation
% 0.17/1.70 % (676597)Time elapsed: 0.189 s
% 0.17/1.70 % (676597)Peak memory usage: 89 MB
% 0.17/1.70 % (676597)Instructions burned: 326 (million)
% 0.17/1.70 % (676596)Refutation found. Thanks to Tanya!
% 0.17/1.70 % SZS status Theorem for theBenchmark
% 0.17/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.70 % (676596)------------------------------
% 0.17/1.70 % (676596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.70 % (676596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.70 % (676596)CaDiCaL version: 2.1.3
% 0.17/1.70 % (676596)Termination reason: Refutation
% 0.17/1.70 % (676596)Time elapsed: 0.007 s
% 0.17/1.70 % (676596)Peak memory usage: 88 MB
% 0.17/1.70 % (676596)Instructions burned: 10 (million)
% 0.17/1.70 % (676596)------------------------------
% 0.17/1.70 % (676596)------------------------------
% 0.17/1.70 % (676576)Success in time 0.639 s
% 0.17/1.70 % Vampire exiting
%------------------------------------------------------------------------------