%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP658+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 : 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 10:15:28 AM UTC 2026
% Result : Theorem 5.16s 1.71s
% Output : Refutation 5.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 29 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 77 ( 74 !; 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(f3,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X0,X1,X2] : mult(mult(X2,mult(X1,X1)),X0) = mult(mult(X2,X1),mult(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,conjecture,
? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f7,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0] :
? [X1] :
( mult(X1,X0) != X1
| mult(X0,X1) != X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
! [X0] :
( sK0(X0) != mult(sK0(X0),X0)
| sK0(X0) != mult(X0,sK0(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f8]) ).
fof(f10,plain,
! [X0] :
( sK0(X0) != mult(sK0(X0),X0)
| sK0(X0) != mult(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f11,plain,
! [X2,X0,X1] : mult(mult(X2,mult(X1,X1)),X0) = mult(mult(X2,X1),mult(X1,X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f12,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f13,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[],[f12,f15]) ).
fof(f19,plain,
! [X2,X0,X1] : mult(mult(rd(X0,mult(X1,X1)),X1),mult(X1,X2)) = mult(X0,X2),
inference(superposition,[],[f11,f13]) ).
fof(f24,plain,
! [X2,X0,X1] : mult(mult(X0,X1),mult(X1,ld(mult(X0,mult(X1,X1)),X2))) = X2,
inference(superposition,[],[f15,f11]) ).
fof(f34,plain,
! [X2,X0,X1] : mult(X1,ld(X2,X0)) = mult(mult(rd(X1,mult(X2,X2)),X2),X0),
inference(superposition,[],[f19,f15]) ).
fof(f107,plain,
! [X2,X0,X1] : mult(X2,ld(mult(X1,mult(X2,X2)),X0)) = ld(mult(X1,X2),X0),
inference(superposition,[],[f14,f24]) ).
fof(f152,plain,
! [X2,X0,X1] : mult(rd(X0,mult(X1,X1)),X1) = rd(mult(X0,ld(X1,X2)),X2),
inference(superposition,[],[f12,f34]) ).
fof(f952,plain,
! [X2,X0,X1] : mult(X1,ld(mult(X0,X1),X2)) = ld(mult(mult(rd(X0,mult(X1,X1)),X1),X1),X2),
inference(superposition,[],[f107,f19]) ).
fof(f1022,plain,
! [X2,X0,X1] : mult(X1,ld(mult(X0,X1),X2)) = ld(mult(X0,ld(X1,X1)),X2),
inference(forward_demodulation,[],[f952,f34]) ).
fof(f1062,plain,
! [X0,X1] : mult(rd(X1,mult(X1,X1)),X1) = rd(X0,X0),
inference(superposition,[],[f152,f15]) ).
fof(f1431,plain,
! [X2,X0,X1] : mult(X1,ld(X1,X2)) = mult(rd(X0,X0),X2),
inference(superposition,[],[f34,f1062]) ).
fof(f1500,plain,
! [X2,X0] : mult(rd(X0,X0),X2) = X2,
inference(forward_demodulation,[],[f1431,f15]) ).
fof(f1887,plain,
! [X2,X0,X1] : mult(X0,mult(X0,ld(mult(rd(X1,X1),mult(X0,X0)),X2))) = X2,
inference(superposition,[],[f24,f1500]) ).
fof(f1943,plain,
! [X2,X0,X1] : mult(X0,ld(mult(rd(X1,X1),X0),X2)) = X2,
inference(forward_demodulation,[],[f1887,f107]) ).
fof(f1986,plain,
! [X2,X0,X1] : ld(mult(rd(X1,X1),ld(X0,X0)),X2) = X2,
inference(forward_demodulation,[],[f1943,f1022]) ).
fof(f2001,plain,
! [X2,X0] : ld(ld(X0,X0),X2) = X2,
inference(forward_demodulation,[],[f1986,f1500]) ).
fof(f2401,plain,
! [X0,X1] : ld(X1,X1) = rd(X0,X0),
inference(superposition,[],[f17,f2001]) ).
fof(f2792,plain,
! [X0,X1] : mult(X1,rd(X0,X0)) = X1,
inference(superposition,[],[f15,f2401]) ).
fof(f4638,plain,
! [X0] :
( sK0(rd(X0,X0)) != sK0(rd(X0,X0))
| sK0(rd(X0,X0)) != mult(rd(X0,X0),sK0(rd(X0,X0))) ),
inference(superposition,[],[f10,f2792]) ).
fof(f4639,plain,
! [X0] : sK0(rd(X0,X0)) != mult(rd(X0,X0),sK0(rd(X0,X0))),
inference(trivial_inequality_removal,[],[f4638]) ).
fof(f4640,plain,
$false,
inference(forward_subsumption_resolution,[],[f4639,f1500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP658+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:32:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 5.16/1.71 % (598173)Detected formulas, will run a generic FOF schedule.
% 5.16/1.71 % (598266)dis-21_1_sil=8000:lcm=predicate:random_seed=3909679421: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)
% 5.16/1.71 % (598266)Refutation not found, incomplete strategy
% 5.16/1.71 % (598266)------------------------------
% 5.16/1.71 % (598266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.71 % (598266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.71 % (598266)CaDiCaL version: 2.1.3
% 5.16/1.71 % (598266)Termination reason: Refutation not found, incomplete strategy
% 5.16/1.71 % (598266)Time elapsed: 0.001 s
% 5.16/1.71 % (598266)Peak memory usage: 88 MB
% 5.16/1.71 % (598264)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3985979053:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.16/1.71 % (598265)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3741155257:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.16/1.71 % (598262)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=443455934:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.16/1.71 % (598260)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=123848975:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.16/1.71 % (598263)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3302127755:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.16/1.71 % (598263)Refutation not found, incomplete strategy
% 5.16/1.71 % (598263)------------------------------
% 5.16/1.71 % (598263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.71 % (598263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.71 % (598263)CaDiCaL version: 2.1.3
% 5.16/1.71 % (598263)Termination reason: Refutation not found, incomplete strategy
% 5.16/1.71 % (598263)Time elapsed: 0.001 s
% 5.16/1.71 % (598263)Peak memory usage: 88 MB
% 5.16/1.71 % (598261)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=2161715739:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.16/1.71 % (598264)Instruction limit reached!
% 5.16/1.71 % (598264)------------------------------
% 5.16/1.71 % (598264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.71 % (598264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.71 % (598264)CaDiCaL version: 2.1.3
% 5.16/1.71 % (598264)Termination reason: Instruction limit
% 5.16/1.71 % (598264)Termination phase: Saturation
% 5.16/1.71 % (598264)Time elapsed: 0.059 s
% 5.16/1.71 % (598264)Peak memory usage: 88 MB
% 5.16/1.71 % (598264)Instructions burned: 120 (million)
% 5.16/1.71 % (598265)Instruction limit reached!
% 5.16/1.71 % (598265)------------------------------
% 5.16/1.71 % (598265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.71 % (598265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.71 % (598265)CaDiCaL version: 2.1.3
% 5.16/1.71 % (598265)Termination reason: Instruction limit
% 5.16/1.71 % (598265)Termination phase: Saturation
% 5.16/1.71 % (598265)Time elapsed: 0.092 s
% 5.16/1.71 % (598265)Peak memory usage: 89 MB
% 5.16/1.71 % (598265)Instructions burned: 139 (million)
% 5.16/1.71 % (598266)------------------------------
% 5.16/1.71 % (598266)------------------------------
% 5.16/1.71 % (598274)lrs+10_1_sil=8000:sp=occurrence:random_seed=3730565454:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.16/1.71 % (598263)------------------------------
% 5.16/1.71 % (598263)------------------------------
% 5.16/1.71 % (598284)lrs+1011_1_sil=32000:sp=occurrence:random_seed=62609045:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.16/1.71 % (598279)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3874786945:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.16/1.71 % (598284)First to succeed.
% 5.16/1.71 % (598284)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-598173"
% 5.16/1.71 % (598274)Also succeeded, but the first one will report.
% 5.16/1.71 % (598279)Instruction limit reached!
% 5.16/1.71 % (598279)------------------------------
% 5.16/1.71 % (598279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.71 % (598279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.71 % (598279)CaDiCaL version: 2.1.3
% 5.16/1.71 % (598279)Termination reason: Instruction limit
% 5.16/1.71 % (598279)Termination phase: Saturation
% 5.16/1.71 % (598279)Time elapsed: 0.093 s
% 5.16/1.71 % (598279)Peak memory usage: 90 MB
% 5.16/1.71 % (598279)Instructions burned: 159 (million)
% 5.16/1.71 % (598288)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=625240707:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.16/1.71 % (598284)Refutation found. Thanks to Tanya!
% 5.16/1.71 % SZS status Theorem for theBenchmark
% 5.16/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 5.16/1.71 % (598284)------------------------------
% 5.16/1.71 % (598284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.71 % (598284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.71 % (598284)CaDiCaL version: 2.1.3
% 5.16/1.71 % (598284)Termination reason: Refutation
% 5.16/1.71 % (598284)Time elapsed: 0.065 s
% 5.16/1.71 % (598284)Peak memory usage: 92 MB
% 5.16/1.71 % (598284)Instructions burned: 209 (million)
% 5.16/1.71 % (598284)------------------------------
% 5.16/1.71 % (598284)------------------------------
% 5.16/1.71 % (598173)Success in time 0.643 s
% 5.16/1.71 % Vampire exiting
%------------------------------------------------------------------------------