%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP001+6 : 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 : n014.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 10:12:04 AM UTC 2026
% Result : Theorem 4.95s 1.65s
% Output : Refutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 149 ( 38 ~; 30 |; 66 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 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 : 178 ( 160 !; 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/sandbox2/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(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,
! [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(f88,plain,
product(sK3,sK2,sK1),
inference(unit_resulting_resolution,[],[f12,f16,f11,f15]) ).
fof(f90,plain,
~ product(sK3,sK1,sK2),
inference(unit_resulting_resolution,[],[f12,f17,f11,f15]) ).
fof(f351,plain,
product(sK3,sK1,sK2),
inference(unit_resulting_resolution,[],[f13,f10,f15,f88]) ).
fof(f392,plain,
$false,
inference(forward_subsumption_resolution,[],[f351,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:12:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 4.95/1.65 % (534977)Detected formulas, will run a generic FOF schedule.
% 4.95/1.65 % (534986)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3646817307:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.95/1.65 % (534986)Instruction limit reached!
% 4.95/1.65 % (534986)------------------------------
% 4.95/1.65 % (534986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.65 % (534986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.65 % (534986)CaDiCaL version: 2.1.3
% 4.95/1.65 % (534986)Termination reason: Instruction limit
% 4.95/1.65 % (534986)Termination phase: Saturation
% 4.95/1.65 % (534986)Time elapsed: 0.036 s
% 4.95/1.65 % (534986)Peak memory usage: 88 MB
% 4.95/1.65 % (534986)Instructions burned: 122 (million)
% 4.95/1.65 % (534988)dis-21_1_sil=8000:lcm=predicate:random_seed=3712683480: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)
% 4.95/1.65 % (534985)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=95931094:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.95/1.65 % (534982)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=845242544:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.95/1.65 % (534983)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=3603876837:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.95/1.65 % (534984)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=111455493:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.95/1.65 % (534987)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2516539359:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.95/1.65 % (534985)Instruction limit reached!
% 4.95/1.65 % (534985)------------------------------
% 4.95/1.65 % (534985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.65 % (534985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.65 % (534985)CaDiCaL version: 2.1.3
% 4.95/1.65 % (534985)Termination reason: Instruction limit
% 4.95/1.65 % (534985)Termination phase: Saturation
% 4.95/1.65 % (534985)Time elapsed: 0.068 s
% 4.95/1.65 % (534985)Peak memory usage: 89 MB
% 4.95/1.65 % (534985)Instructions burned: 110 (million)
% 4.95/1.65 % (534988)Instruction limit reached!
% 4.95/1.65 % (534988)------------------------------
% 4.95/1.65 % (534988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.65 % (534988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.65 % (534988)CaDiCaL version: 2.1.3
% 4.95/1.65 % (534988)Termination reason: Instruction limit
% 4.95/1.65 % (534988)Termination phase: Saturation
% 4.95/1.65 % (534988)Time elapsed: 0.073 s
% 4.95/1.65 % (534988)Peak memory usage: 89 MB
% 4.95/1.65 % (534988)Instructions burned: 130 (million)
% 4.95/1.65 % (534995)lrs+10_1_sil=8000:sp=occurrence:random_seed=3004896351:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.95/1.65 % (534987)Instruction limit reached!
% 4.95/1.65 % (534987)------------------------------
% 4.95/1.65 % (534987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.65 % (534987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.65 % (534987)CaDiCaL version: 2.1.3
% 4.95/1.65 % (534987)Termination reason: Instruction limit
% 4.95/1.65 % (534987)Termination phase: Saturation
% 4.95/1.65 % (534987)Time elapsed: 0.083 s
% 4.95/1.65 % (534987)Peak memory usage: 89 MB
% 4.95/1.65 % (534987)Instructions burned: 139 (million)
% 4.95/1.65 % (534995)Instruction limit reached!
% 4.95/1.65 % (534995)------------------------------
% 4.95/1.65 % (534995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.65 % (534995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.65 % (534995)CaDiCaL version: 2.1.3
% 4.95/1.65 % (534995)Termination reason: Instruction limit
% 4.95/1.65 % (534995)Termination phase: Saturation
% 4.95/1.65 % (534995)Time elapsed: 0.096 s
% 4.95/1.65 % (534995)Peak memory usage: 90 MB
% 4.95/1.65 % (534995)Instructions burned: 286 (million)
% 4.95/1.65 % (534998)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2848286062:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.95/1.65 % (534997)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3514997044:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.95/1.65 % (534997)First to succeed.
% 4.95/1.65 % (534997)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-534977"
% 4.95/1.65 % (535000)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=36600350:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.95/1.65 % (535000)Also succeeded, but the first one will report.
% 4.95/1.65 % (535001)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=536151842:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.95/1.65 % (535001)Instruction limit reached!
% 4.95/1.65 % (535001)------------------------------
% 4.95/1.65 % (535001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.65 % (535001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.65 % (535001)CaDiCaL version: 2.1.3
% 4.95/1.65 % (535001)Termination reason: Instruction limit
% 4.95/1.65 % (535001)Termination phase: Saturation
% 4.95/1.65 % (535001)Time elapsed: 0.068 s
% 4.95/1.65 % (535001)Peak memory usage: 88 MB
% 4.95/1.65 % (535001)Instructions burned: 295 (million)
% 4.95/1.65 % (534998)Instruction limit reached!
% 4.95/1.65 % (534998)------------------------------
% 4.95/1.65 % (534998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.65 % (534998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.65 % (534998)CaDiCaL version: 2.1.3
% 4.95/1.65 % (534998)Termination reason: Instruction limit
% 4.95/1.65 % (534998)Termination phase: Saturation
% 4.95/1.65 % (534998)Time elapsed: 0.179 s
% 4.95/1.65 % (534998)Peak memory usage: 90 MB
% 4.95/1.65 % (534998)Instructions burned: 326 (million)
% 4.95/1.65 % (535007)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=449091621:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.95/1.65 % (534997)Refutation found. Thanks to Tanya!
% 4.95/1.65 % SZS status Theorem for theBenchmark
% 4.95/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 4.95/1.65 % (534997)------------------------------
% 4.95/1.65 % (534997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.65 % (534997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.65 % (534997)CaDiCaL version: 2.1.3
% 4.95/1.65 % (534997)Termination reason: Refutation
% 4.95/1.65 % (534997)Time elapsed: 0.007 s
% 4.95/1.65 % (534997)Peak memory usage: 89 MB
% 4.95/1.65 % (534997)Instructions burned: 10 (million)
% 4.95/1.65 % (534997)------------------------------
% 4.95/1.65 % (534997)------------------------------
% 4.95/1.65 % (534977)Success in time 0.613 s
% 4.95/1.65 % Vampire exiting
%------------------------------------------------------------------------------