%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP703+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:16:00 AM UTC 2026
% Result : Theorem 3.53s 1.54s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 25 unt; 3 def)
% Number of atoms : 70 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 19 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f5,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f6,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f8,axiom,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(op_c,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f9,axiom,
! [X0,X1] : mult(X1,mult(X0,op_c)) = mult(mult(X1,X0),op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
fof(f10,axiom,
! [X0,X1] : mult(X1,mult(op_c,X0)) = mult(mult(X1,op_c),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
fof(f12,axiom,
! [X0,X1] : op_e = mult(mult(rd(op_c,mult(X1,X0)),X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f12) ).
fof(f14,conjecture,
! [X0,X1] :
( mult(op_e,mult(X0,X1)) = mult(mult(op_e,X0),X1)
& mult(X0,mult(X1,op_e)) = mult(mult(X0,X1),op_e)
& mult(X0,mult(op_e,X1)) = mult(mult(X0,op_e),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( mult(op_e,mult(X0,X1)) = mult(mult(op_e,X0),X1)
& mult(X0,mult(X1,op_e)) = mult(mult(X0,X1),op_e)
& mult(X0,mult(op_e,X1)) = mult(mult(X0,op_e),X1) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( mult(op_e,mult(X0,X1)) != mult(mult(op_e,X0),X1)
| mult(X0,mult(X1,op_e)) != mult(mult(X0,X1),op_e)
| mult(X0,mult(op_e,X1)) != mult(mult(X0,op_e),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( mult(op_e,mult(sK0,sK1)) != mult(mult(op_e,sK0),sK1)
| mult(sK0,mult(sK1,op_e)) != mult(mult(sK0,sK1),op_e)
| mult(sK0,mult(op_e,sK1)) != mult(mult(sK0,op_e),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f20,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[],[f5]) ).
fof(f23,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(op_c,X1),X0),
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] : mult(X1,mult(X0,op_c)) = mult(mult(X1,X0),op_c),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : mult(X1,mult(op_c,X0)) = mult(mult(X1,op_c),X0),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] : op_e = mult(mult(rd(op_c,mult(X1,X0)),X0),X1),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
( mult(op_e,mult(sK0,sK1)) != mult(mult(op_e,sK0),sK1)
| mult(sK0,mult(sK1,op_e)) != mult(mult(sK0,sK1),op_e)
| mult(sK0,mult(op_e,sK1)) != mult(mult(sK0,op_e),sK1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,definition,
( spl2_1
<=> mult(sK0,mult(op_e,sK1)) = mult(mult(sK0,op_e),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f35,plain,
( mult(sK0,mult(op_e,sK1)) != mult(mult(sK0,op_e),sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,definition,
( spl2_2
<=> mult(sK0,mult(sK1,op_e)) = mult(mult(sK0,sK1),op_e) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f39,plain,
( mult(sK0,mult(sK1,op_e)) != mult(mult(sK0,sK1),op_e)
| spl2_2 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl2_3
<=> mult(op_e,mult(sK0,sK1)) = mult(mult(op_e,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f43,plain,
( mult(op_e,mult(sK0,sK1)) != mult(mult(op_e,sK0),sK1)
| spl2_3 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f31,f41,f37,f33]) ).
fof(f126,plain,
! [X0] : op_e = mult(rd(op_c,mult(unit,X0)),X0),
inference(superposition,[],[f22,f29]) ).
fof(f128,plain,
! [X0] : op_e = mult(rd(op_c,X0),X0),
inference(forward_demodulation,[],[f126,f23]) ).
fof(f134,plain,
op_c = op_e,
inference(forward_demodulation,[],[f128,f20]) ).
fof(f139,plain,
( mult(sK0,mult(op_c,sK1)) != mult(mult(sK0,op_c),sK1)
| spl2_1 ),
inference(superposition,[],[f35,f134]) ).
fof(f140,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f139,f27]) ).
fof(f141,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f143,plain,
( mult(sK0,mult(sK1,op_c)) != mult(mult(sK0,sK1),op_c)
| spl2_2 ),
inference(forward_demodulation,[],[f39,f134]) ).
fof(f144,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f143,f26]) ).
fof(f145,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f144]) ).
fof(f147,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| spl2_3 ),
inference(forward_demodulation,[],[f43,f134]) ).
fof(f148,plain,
( $false
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f147,f25]) ).
fof(f149,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f148]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f141]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f145]) ).
cnf(s4,plain,
spl2_3,
inference(sat_conversion,[],[f149]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f150,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP703+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n026.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 10:39:27 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.45 Running first-order theorem proving
% 0.10/0.45 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
% 3.53/1.54 % (2643026)Detected formulas, will run a generic FOF schedule.
% 3.53/1.54 % (2643040)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=1722132893:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.54 % (2643046)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4202126886:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.54 % (2643044)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3952817892:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.54 % (2643043)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=349998867:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.54 % (2643047)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3807172310:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.54 % (2643047)First to succeed.
% 3.53/1.54 % (2643046)Also succeeded, but the first one will report.
% 3.53/1.54 % (2643047)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2643026"
% 3.53/1.54 % (2643041)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=1204938153:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.54 % (2643048)dis-21_1_sil=8000:lcm=predicate:random_seed=2332879833: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)
% 3.53/1.54 % (2643048)Refutation not found, incomplete strategy
% 3.53/1.54 % (2643048)------------------------------
% 3.53/1.54 % (2643048)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.54 % (2643048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.54 % (2643048)CaDiCaL version: 2.1.3
% 3.53/1.54 % (2643048)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.54 % (2643048)Time elapsed: 0.002 s
% 3.53/1.54 % (2643048)Peak memory usage: 88 MB
% 3.53/1.54 % (2643048)Instructions burned: 1 (million)
% 3.53/1.54 % (2643044)Instruction limit reached!
% 3.53/1.54 % (2643044)------------------------------
% 3.53/1.54 % (2643044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.54 % (2643044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.54 % (2643044)CaDiCaL version: 2.1.3
% 3.53/1.54 % (2643044)Termination reason: Instruction limit
% 3.53/1.54 % (2643044)Termination phase: Saturation
% 3.53/1.54 % (2643044)Time elapsed: 0.063 s
% 3.53/1.54 % (2643044)Peak memory usage: 89 MB
% 3.53/1.54 % (2643044)Instructions burned: 110 (million)
% 3.53/1.54 % (2643119)lrs+10_1_sil=8000:sp=occurrence:random_seed=1599664662:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.54 % (2643119)Also succeeded, but the first one will report.
% 3.53/1.54 % (2643047)Refutation found. Thanks to Tanya!
% 3.53/1.54 % SZS status Theorem for theBenchmark
% 3.53/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.54 % (2643047)------------------------------
% 3.53/1.54 % (2643047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.54 % (2643047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.54 % (2643047)CaDiCaL version: 2.1.3
% 3.53/1.54 % (2643047)Termination reason: Refutation
% 3.53/1.54 % (2643047)Time elapsed: 0.006 s
% 3.53/1.54 % (2643047)Peak memory usage: 89 MB
% 3.53/1.54 % (2643047)Instructions burned: 6 (million)
% 3.53/1.54 % (2643047)------------------------------
% 3.53/1.54 % (2643047)------------------------------
% 3.53/1.54 % (2643026)Success in time 0.399 s
% 3.53/1.54 % Vampire exiting
%------------------------------------------------------------------------------