%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 10:15:58 AM UTC 2026
% Result : Theorem 11.93s 2.71s
% Output : Refutation 11.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f5,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f8,axiom,
! [X0,X1,X2] : mult(mult(X2,X1),mult(X1,mult(X0,X1))) = mult(mult(X2,mult(X1,mult(X1,X0))),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f9,conjecture,
! [X0] :
? [X1] :
( mult(X1,X0) = unit
& mult(X0,X1) = unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f10,negated_conjecture,
~ ! [X0] :
? [X1] :
( mult(X1,X0) = unit
& mult(X0,X1) = unit ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
? [X0] :
! [X1] :
( mult(X1,X0) != unit
| unit != mult(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f12,plain,
! [X1] :
( unit != mult(X1,sK0)
| unit != mult(sK0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f11]) ).
fof(f13,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[],[f5]) ).
fof(f20,plain,
! [X2,X0,X1] : mult(mult(X2,X1),mult(X1,mult(X0,X1))) = mult(mult(X2,mult(X1,mult(X1,X0))),X1),
inference(cnf_transformation,[],[f8]) ).
fof(f21,plain,
! [X1] :
( unit != mult(X1,sK0)
| unit != mult(sK0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X0,X1] : mult(mult(X1,X2),mult(X2,mult(ld(X2,X0),X2))) = mult(mult(X1,mult(X2,X0)),X2),
inference(superposition,[],[f20,f13]) ).
fof(f44,plain,
! [X0] : unit = ld(X0,X0),
inference(superposition,[],[f14,f17]) ).
fof(f201,plain,
! [X2,X0,X1] : mult(X1,mult(ld(X1,X2),X1)) = ld(mult(X0,X1),mult(mult(X0,mult(X1,X2)),X1)),
inference(superposition,[],[f14,f27]) ).
fof(f240,plain,
! [X0,X1] : mult(X0,mult(ld(X0,unit),X0)) = ld(mult(X1,X0),mult(mult(X1,X0),X0)),
inference(superposition,[],[f201,f17]) ).
fof(f266,plain,
! [X0] : mult(X0,mult(ld(X0,unit),X0)) = X0,
inference(forward_demodulation,[],[f240,f14]) ).
fof(f290,plain,
! [X0] : ld(X0,X0) = mult(ld(X0,unit),X0),
inference(superposition,[],[f14,f266]) ).
fof(f309,plain,
! [X0] : unit = mult(ld(X0,unit),X0),
inference(forward_demodulation,[],[f290,f44]) ).
fof(f317,plain,
$false,
inference(unit_resulting_resolution,[],[f21,f13,f309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n009.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 10:36:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.99/2.46 % (1840085)Detected formulas, will run a generic FOF schedule.
% 10.99/2.46 % (1840170)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=2465745018:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.99/2.46 % (1840173)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2944826591:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.99/2.46 % (1840174)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=836765002:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.99/2.46 % (1840176)dis-21_1_sil=8000:lcm=predicate:random_seed=151994758: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)
% 10.99/2.46 % (1840171)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=445546750:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.99/2.46 % (1840172)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=2152742744:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.99/2.46 % (1840176)Refutation not found, incomplete strategy
% 10.99/2.46 % (1840176)------------------------------
% 10.99/2.46 % (1840176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.46 % (1840176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.46 % (1840176)CaDiCaL version: 2.1.3
% 10.99/2.46 % (1840176)Termination reason: Refutation not found, incomplete strategy
% 10.99/2.46 % (1840176)Time elapsed: 0.002 s
% 10.99/2.46 % (1840176)Peak memory usage: 88 MB
% 10.99/2.46 % (1840176)Instructions burned: 1 (million)
% 10.99/2.46 % (1840175)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2508570022:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.99/2.46 % (1840173)Instruction limit reached!
% 10.99/2.46 % (1840173)------------------------------
% 10.99/2.46 % (1840173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.46 % (1840173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.46 % (1840173)CaDiCaL version: 2.1.3
% 10.99/2.46 % (1840173)Termination reason: Instruction limit
% 10.99/2.46 % (1840173)Termination phase: Saturation
% 10.99/2.46 % (1840173)Time elapsed: 0.107 s
% 10.99/2.46 % (1840173)Peak memory usage: 89 MB
% 10.99/2.46 % (1840173)Instructions burned: 110 (million)
% 10.99/2.46 % (1840174)Instruction limit reached!
% 10.99/2.46 % (1840174)------------------------------
% 10.99/2.46 % (1840174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.46 % (1840174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.46 % (1840174)CaDiCaL version: 2.1.3
% 10.99/2.46 % (1840174)Termination reason: Instruction limit
% 10.99/2.46 % (1840174)Termination phase: Saturation
% 10.99/2.46 % (1840174)Time elapsed: 0.111 s
% 10.99/2.46 % (1840174)Peak memory usage: 88 MB
% 10.99/2.46 % (1840174)Instructions burned: 120 (million)
% 10.99/2.46 % (1840175)Instruction limit reached!
% 10.99/2.46 % (1840175)------------------------------
% 10.99/2.46 % (1840175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.99/2.46 % (1840175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.99/2.46 % (1840175)CaDiCaL version: 2.1.3
% 10.99/2.46 % (1840175)Termination reason: Instruction limit
% 10.99/2.46 % (1840175)Termination phase: Saturation
% 10.99/2.46 % (1840175)Time elapsed: 0.131 s
% 10.99/2.46 % (1840175)Peak memory usage: 89 MB
% 10.99/2.46 % (1840175)Instructions burned: 140 (million)
% 10.99/2.46 % (1840176)------------------------------
% 10.99/2.46 % (1840176)------------------------------
% 10.99/2.46 % (1840214)lrs+10_1_sil=8000:sp=occurrence:random_seed=3635976614:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 10.99/2.46 % (1840216)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3638204910:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 10.99/2.46 % (1840220)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2846737162:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 10.99/2.46 % (1840216)Instruction limit reached!
% 10.99/2.46 % (1840216)------------------------------
% 10.99/2.46 % (1840216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840216)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840216)Termination reason: Instruction limit
% 11.93/2.71 % (1840216)Termination phase: Saturation
% 11.93/2.71 % (1840216)Time elapsed: 0.148 s
% 11.93/2.71 % (1840216)Peak memory usage: 90 MB
% 11.93/2.71 % (1840216)Instructions burned: 157 (million)
% 11.93/2.71 % (1840224)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=3397829495:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 11.93/2.71 % (1840214)Instruction limit reached!
% 11.93/2.71 % (1840214)------------------------------
% 11.93/2.71 % (1840214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840214)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840214)Termination reason: Instruction limit
% 11.93/2.71 % (1840214)Termination phase: Saturation
% 11.93/2.71 % (1840214)Time elapsed: 0.272 s
% 11.93/2.71 % (1840214)Peak memory usage: 92 MB
% 11.93/2.71 % (1840214)Instructions burned: 285 (million)
% 11.93/2.71 % (1840220)Instruction limit reached!
% 11.93/2.71 % (1840220)------------------------------
% 11.93/2.71 % (1840220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840220)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840220)Termination reason: Instruction limit
% 11.93/2.71 % (1840220)Termination phase: Saturation
% 11.93/2.71 % (1840220)Time elapsed: 0.312 s
% 11.93/2.71 % (1840220)Peak memory usage: 92 MB
% 11.93/2.71 % (1840220)Instructions burned: 325 (million)
% 11.93/2.71 % (1840230)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=580205514:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 11.93/2.71 % (1840224)Instruction limit reached!
% 11.93/2.71 % (1840224)------------------------------
% 11.93/2.71 % (1840224)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840224)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840224)Termination reason: Instruction limit
% 11.93/2.71 % (1840224)Termination phase: Saturation
% 11.93/2.71 % (1840224)Time elapsed: 0.234 s
% 11.93/2.71 % (1840224)Peak memory usage: 91 MB
% 11.93/2.71 % (1840224)Instructions burned: 248 (million)
% 11.93/2.71 % (1840232)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1500305782:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 11.93/2.71 % (1840171)First to succeed.
% 11.93/2.71 % (1840171)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1840085"
% 11.93/2.71 % (1840234)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3419348158:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 11.93/2.71 % (1840234)Refutation not found, incomplete strategy
% 11.93/2.71 % (1840234)------------------------------
% 11.93/2.71 % (1840234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840234)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840234)Termination reason: Refutation not found, incomplete strategy
% 11.93/2.71 % (1840234)Time elapsed: 0.003 s
% 11.93/2.71 % (1840234)Peak memory usage: 88 MB
% 11.93/2.71 % (1840172)Refutation not found, incomplete strategy
% 11.93/2.71 % (1840172)------------------------------
% 11.93/2.71 % (1840172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840172)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840172)Termination reason: Refutation not found, incomplete strategy
% 11.93/2.71 % (1840172)Time elapsed: 0.985 s
% 11.93/2.71 % (1840172)Peak memory usage: 128 MB
% 11.93/2.71 % (1840172)Instructions burned: 891 (million)
% 11.93/2.71 % (1840230)Instruction limit reached!
% 11.93/2.71 % (1840230)------------------------------
% 11.93/2.71 % (1840230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840230)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840230)Termination reason: Instruction limit
% 11.93/2.71 % (1840230)Termination phase: Saturation
% 11.93/2.71 % (1840230)Time elapsed: 0.272 s
% 11.93/2.71 % (1840230)Peak memory usage: 90 MB
% 11.93/2.71 % (1840230)Instructions burned: 294 (million)
% 11.93/2.71 % (1840241)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2099966922:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 11.93/2.71 % (1840241)Refutation not found, incomplete strategy
% 11.93/2.71 % (1840241)------------------------------
% 11.93/2.71 % (1840241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840241)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840241)Termination reason: Refutation not found, incomplete strategy
% 11.93/2.71 % (1840241)Time elapsed: 0.001 s
% 11.93/2.71 % (1840241)Peak memory usage: 88 MB
% 11.93/2.71 % (1840170)Also succeeded, but the first one will report.
% 11.93/2.71 % (1840234)------------------------------
% 11.93/2.71 % (1840234)------------------------------
% 11.93/2.71 % (1840246)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3629841583:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2987 on theBenchmark for (2987ds/114Mi)
% 11.93/2.71 % (1840246)Refutation not found, incomplete strategy
% 11.93/2.71 % (1840246)------------------------------
% 11.93/2.71 % (1840246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840246)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840246)Termination reason: Refutation not found, incomplete strategy
% 11.93/2.71 % (1840246)Time elapsed: 0.002 s
% 11.93/2.71 % (1840246)Peak memory usage: 88 MB
% 11.93/2.71 % (1840172)------------------------------
% 11.93/2.71 % (1840172)------------------------------
% 11.93/2.71 % (1840171)Refutation found. Thanks to Tanya!
% 11.93/2.71 % SZS status Theorem for theBenchmark
% 11.93/2.71 % SZS output start Proof for theBenchmark
% See solution above
% 11.93/2.71 % (1840171)------------------------------
% 11.93/2.71 % (1840171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.93/2.71 % (1840171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.93/2.71 % (1840171)CaDiCaL version: 2.1.3
% 11.93/2.71 % (1840171)Termination reason: Refutation
% 11.93/2.71 % (1840171)Time elapsed: 0.958 s
% 11.93/2.71 % (1840171)Peak memory usage: 128 MB
% 11.93/2.71 % (1840171)Instructions burned: 987 (million)
% 11.93/2.71 % (1840171)------------------------------
% 11.93/2.71 % (1840171)------------------------------
% 11.93/2.71 % (1840085)Success in time 1.592 s
% 11.93/2.71 % Vampire exiting
%------------------------------------------------------------------------------