%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP665+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 : 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 10:15:31 AM UTC 2026
% Result : Theorem 2.78s 1.37s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 27 unt; 3 def)
% Number of atoms : 80 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 23 |; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f7,axiom,
! [X0,X1,X2] : mult(X2,mult(X1,X0)) = mult(rd(mult(X2,X1),X2),mult(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f8,axiom,
! [X0,X1,X2] : mult(mult(X2,X1),X0) = mult(mult(X2,X0),ld(X0,mult(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f9,axiom,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
fof(f10,conjecture,
! [X0,X1] :
( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c)) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
? [X0,X1] :
( mult(op_c,mult(X0,X1)) != mult(mult(op_c,X0),X1)
| mult(mult(X0,op_c),X1) != mult(X0,mult(op_c,X1))
| mult(mult(X0,X1),op_c) != mult(X0,mult(X1,op_c)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f13,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
fof(f14,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X2,X0,X1] : mult(X2,mult(X1,X0)) = mult(rd(mult(X2,X1),X2),mult(X2,X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X2,X0,X1] : mult(mult(X2,X1),X0) = mult(mult(X2,X0),ld(X0,mult(X1,X0))),
inference(cnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
inference(cnf_transformation,[],[f9]) ).
fof(f23,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,definition,
( spl2_1
<=> mult(mult(sK0,sK1),op_c) = mult(sK0,mult(sK1,op_c)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f27,plain,
( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c))
| spl2_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl2_2
<=> mult(mult(sK0,op_c),sK1) = mult(sK0,mult(op_c,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f31,plain,
( mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| spl2_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl2_3
<=> mult(op_c,mult(sK0,sK1)) = mult(mult(op_c,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f35,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| spl2_3 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f23,f33,f29,f25]) ).
fof(f60,plain,
( mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(sK1,op_c))
| spl2_1 ),
inference(superposition,[],[f27,f22]) ).
fof(f63,plain,
( mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_c,sK1))
| spl2_1 ),
inference(forward_demodulation,[],[f60,f22]) ).
fof(f70,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(rd(mult(X0,op_c),op_c),mult(op_c,X1)),
inference(superposition,[],[f20,f22]) ).
fof(f84,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(X0,mult(op_c,X1)),
inference(forward_demodulation,[],[f70,f17]) ).
fof(f98,plain,
! [X0,X1] : mult(mult(op_c,X1),X0) = mult(mult(X0,op_c),ld(X0,mult(X1,X0))),
inference(superposition,[],[f21,f22]) ).
fof(f106,plain,
! [X0,X1] : mult(mult(X1,op_c),X0) = mult(mult(X1,X0),ld(X0,mult(X0,op_c))),
inference(superposition,[],[f21,f22]) ).
fof(f113,plain,
! [X0,X1] : mult(mult(X1,X0),op_c) = mult(mult(X1,op_c),X0),
inference(forward_demodulation,[],[f106,f15]) ).
fof(f121,plain,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(X1,op_c),X0),
inference(forward_demodulation,[],[f113,f22]) ).
fof(f211,plain,
( mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1))
| spl2_1 ),
inference(superposition,[],[f63,f84]) ).
fof(f212,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[],[f211]) ).
fof(f213,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f212]) ).
fof(f223,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(sK0,op_c),sK1)
| spl2_2 ),
inference(forward_demodulation,[],[f31,f84]) ).
fof(f225,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| spl2_2 ),
inference(forward_demodulation,[],[f223,f22]) ).
fof(f226,plain,
( ~ spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f225,f29,f33]) ).
fof(f770,plain,
! [X0,X1] : mult(mult(op_c,X1),X0) = mult(op_c,mult(X0,ld(X0,mult(X1,X0)))),
inference(forward_demodulation,[],[f98,f121]) ).
fof(f771,plain,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(op_c,X1),X0),
inference(forward_demodulation,[],[f770,f14]) ).
fof(f786,plain,
( mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1))
| spl2_3 ),
inference(superposition,[],[f35,f771]) ).
fof(f810,plain,
( $false
| spl2_3 ),
inference(trivial_inequality_removal,[],[f786]) ).
fof(f811,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f810]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f213]) ).
cnf(s3,plain,
( spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f226]) ).
cnf(s4,plain,
spl2_3,
inference(sat_conversion,[],[f811]) ).
cnf(s5,plain,
spl2_2,
inference(rat,[],[s3,s4]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s5,s2]) ).
fof(f845,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP665+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % 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 10:34:01 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 2.78/1.37 % (766392)Detected formulas, will run a generic FOF schedule.
% 2.78/1.37 % (766402)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=897794586:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.37 % (766402)First to succeed.
% 2.78/1.37 % (766402)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-766392"
% 2.78/1.37 % (766397)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=3015475253:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.37 % (766398)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=1089639241:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.37 % (766399)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=2154957878:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.37 % (766400)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3811095851:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.37 % (766401)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2103361093:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.37 % (766401)Refutation not found, incomplete strategy
% 2.78/1.37 % (766401)------------------------------
% 2.78/1.37 % (766401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (766401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (766400)Refutation not found, incomplete strategy
% 2.78/1.37 % (766400)------------------------------
% 2.78/1.37 % (766400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (766401)CaDiCaL version: 2.1.3
% 2.78/1.37 % (766401)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.37 % (766401)Time elapsed: 0.001 s
% 2.78/1.37 % (766401)Peak memory usage: 88 MB
% 2.78/1.37 % (766400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (766400)CaDiCaL version: 2.1.3
% 2.78/1.37 % (766400)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.37 % (766400)Time elapsed: 0.002 s
% 2.78/1.37 % (766400)Peak memory usage: 88 MB
% 2.78/1.37 % (766403)dis-21_1_sil=8000:lcm=predicate:random_seed=1622413857: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)
% 2.78/1.37 % (766403)Refutation not found, incomplete strategy
% 2.78/1.37 % (766403)------------------------------
% 2.78/1.37 % (766403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (766403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (766403)CaDiCaL version: 2.1.3
% 2.78/1.37 % (766403)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.37 % (766403)Time elapsed: 0.002 s
% 2.78/1.37 % (766403)Peak memory usage: 88 MB
% 2.78/1.37 % (766402)Refutation found. Thanks to Tanya!
% 2.78/1.37 % SZS status Theorem for theBenchmark
% 2.78/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.37 % (766402)------------------------------
% 2.78/1.37 % (766402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (766402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (766402)CaDiCaL version: 2.1.3
% 2.78/1.37 % (766402)Termination reason: Refutation
% 2.78/1.37 % (766402)Time elapsed: 0.012 s
% 2.78/1.37 % (766402)Peak memory usage: 90 MB
% 2.78/1.37 % (766402)Instructions burned: 35 (million)
% 2.78/1.37 % (766402)------------------------------
% 2.78/1.37 % (766402)------------------------------
% 2.78/1.37 % (766392)Success in time 0.307 s
% 2.78/1.37 % Vampire exiting
%------------------------------------------------------------------------------