%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 10:18:36 AM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 19 unt; 3 def)
% Number of atoms : 66 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 20 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f8,axiom,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(op_c,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f9,axiom,
! [X0,X1] : mult(X1,mult(X0,op_c)) = mult(mult(X1,X0),op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(f10,axiom,
! [X0,X1] : mult(X1,mult(op_c,X0)) = mult(mult(X1,op_c),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f11,axiom,
! [X0] : op_d = ld(X0,mult(op_c,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
fof(f14,conjecture,
! [X0,X1] :
( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( mult(op_d,mult(X0,X1)) != mult(mult(op_d,X0),X1)
| mult(X0,mult(X1,op_d)) != mult(mult(X0,X1),op_d)
| mult(X0,mult(op_d,X1)) != mult(mult(X0,op_d),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( mult(op_d,mult(sK0,sK1)) != mult(mult(op_d,sK0),sK1)
| mult(sK0,mult(sK1,op_d)) != mult(mult(sK0,sK1),op_d)
| mult(sK0,mult(op_d,sK1)) != mult(mult(sK0,op_d),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f19,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
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(f28,plain,
! [X0] : op_d = ld(X0,mult(op_c,X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f31,plain,
( mult(op_d,mult(sK0,sK1)) != mult(mult(op_d,sK0),sK1)
| mult(sK0,mult(sK1,op_d)) != mult(mult(sK0,sK1),op_d)
| mult(sK0,mult(op_d,sK1)) != mult(mult(sK0,op_d),sK1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,definition,
( spl2_1
<=> mult(sK0,mult(op_d,sK1)) = mult(mult(sK0,op_d),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f35,plain,
( mult(sK0,mult(op_d,sK1)) != mult(mult(sK0,op_d),sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,definition,
( spl2_2
<=> mult(sK0,mult(sK1,op_d)) = mult(mult(sK0,sK1),op_d) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f39,plain,
( mult(sK0,mult(sK1,op_d)) != mult(mult(sK0,sK1),op_d)
| spl2_2 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl2_3
<=> mult(op_d,mult(sK0,sK1)) = mult(mult(op_d,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f43,plain,
( mult(op_d,mult(sK0,sK1)) != mult(mult(op_d,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(f65,plain,
op_c = op_d,
inference(superposition,[],[f28,f19]) ).
fof(f72,plain,
( mult(sK0,mult(op_c,sK1)) != mult(mult(sK0,op_c),sK1)
| spl2_1 ),
inference(superposition,[],[f35,f65]) ).
fof(f100,plain,
( mult(sK0,mult(op_c,sK1)) != mult(sK0,mult(op_c,sK1))
| spl2_1 ),
inference(superposition,[],[f72,f27]) ).
fof(f106,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[],[f100]) ).
fof(f107,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f106]) ).
fof(f114,plain,
( mult(sK0,mult(sK1,op_c)) != mult(mult(sK0,sK1),op_c)
| spl2_2 ),
inference(forward_demodulation,[],[f39,f65]) ).
fof(f115,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f114,f26]) ).
fof(f116,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f115]) ).
fof(f118,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| spl2_3 ),
inference(forward_demodulation,[],[f43,f65]) ).
fof(f119,plain,
( $false
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f118,f25]) ).
fof(f120,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f119]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f107]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f116]) ).
cnf(s4,plain,
spl2_3,
inference(sat_conversion,[],[f120]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f121,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.37 % Computer : n005.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8046.5625MB
% 0.14/0.37 % OS : Linux 6.8.0-71-generic
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sun Sep 27 10:36:47 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41 Running first-order model finding
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.45 % (3800438)Will run a generic schedule for satisfiability detection.
% 0.14/0.45 % (3800451)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3115854736:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.45 % (3800447)% WARNING: option uhcvi not known.
% 0.14/0.45 % (3800446)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3840360647_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.45 % (3800447)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2735003900:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.45 % (3800452)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2603903108:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.45 % (3800448)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=636468749:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.45 % (3800450)dis+10_1_sil=32000:sp=arity:random_seed=3657567042:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.45 % (3800453)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4256980746:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.45 % TRYING [1]
% 0.14/0.45 % TRYING [2]
% 0.14/0.45 % TRYING [3]
% 0.14/0.45 % (3800450) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3800438-3800450"...
% 0.14/0.45 % (3800450)...printing done.
% 0.14/0.45 % (3800447) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3800438-3800447"...
% 0.14/0.45 % (3800450)Refutation found. Thanks to Tanya!
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (3800450)------------------------------
% 0.14/0.45 % (3800450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (3800450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (3800450)CaDiCaL version: 2.1.3
% 0.14/0.45 % (3800450)Termination reason: Refutation
% 0.14/0.45 % (3800450)Time elapsed: 0.004 s
% 0.14/0.45 % (3800450)Peak memory usage: 12 MB
% 0.14/0.45 % (3800450)Instructions burned: 5 (million)
% 0.14/0.45 % (3800438)Success in time 0.029 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------