%------------------------------------------------------------------------------
% File : Vampire-SAT---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 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 10:18:29 AM UTC 2026
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 30 unt; 3 def)
% Number of atoms : 72 ( 43 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 19 ~; 17 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 50 ( 0 sgn 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(f14,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X2,X0,X1] : mult(X2,mult(X1,X0)) = mult(rd(mult(X2,X1),X2),mult(X2,X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X2,X0,X1] : mult(mult(X2,X1),X0) = mult(mult(X2,X0),ld(X0,mult(X1,X0))),
inference(cnf_transformation,[],[f8]) ).
fof(f21,plain,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c))
| mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,definition,
( spl2_1
<=> mult(op_c,mult(sK0,sK1)) = mult(mult(op_c,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f26,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,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(f30,plain,
( mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| spl2_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f32,definition,
( spl2_3
<=> mult(mult(sK0,sK1),op_c) = mult(sK0,mult(sK1,op_c)) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f34,plain,
( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c))
| spl2_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f22,f32,f28,f24]) ).
fof(f57,plain,
! [X0] : ld(op_c,mult(X0,op_c)) = X0,
inference(superposition,[],[f14,f21]) ).
fof(f58,plain,
! [X0] : rd(mult(op_c,X0),op_c) = X0,
inference(superposition,[],[f16,f21]) ).
fof(f72,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(rd(mult(X0,op_c),op_c),mult(op_c,X1)),
inference(superposition,[],[f19,f21]) ).
fof(f80,plain,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(rd(mult(op_c,X1),op_c),mult(X0,op_c)),
inference(superposition,[],[f19,f21]) ).
fof(f83,plain,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(X1,mult(X0,op_c)),
inference(forward_demodulation,[],[f80,f58]) ).
fof(f87,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(X0,mult(op_c,X1)),
inference(forward_demodulation,[],[f72,f16]) ).
fof(f102,plain,
! [X0,X1] : mult(mult(X0,X1),op_c) = mult(mult(op_c,X0),ld(op_c,mult(X1,op_c))),
inference(superposition,[],[f20,f21]) ).
fof(f115,plain,
! [X0,X1] : mult(mult(X1,op_c),X0) = mult(mult(X1,X0),ld(X0,mult(X0,op_c))),
inference(superposition,[],[f20,f21]) ).
fof(f124,plain,
! [X0,X1] : mult(mult(X1,X0),op_c) = mult(mult(X1,op_c),X0),
inference(forward_demodulation,[],[f115,f14]) ).
fof(f130,plain,
! [X0,X1] : mult(mult(op_c,X0),X1) = mult(mult(X0,X1),op_c),
inference(forward_demodulation,[],[f102,f57]) ).
fof(f133,plain,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(X1,op_c),X0),
inference(forward_demodulation,[],[f124,f21]) ).
fof(f137,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
inference(forward_demodulation,[],[f130,f21]) ).
fof(f390,plain,
( mult(op_c,mult(sK0,sK1)) != mult(op_c,mult(sK0,sK1))
| spl2_1 ),
inference(superposition,[],[f26,f137]) ).
fof(f407,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[],[f390]) ).
fof(f408,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f407]) ).
fof(f430,plain,
( mult(mult(sK0,op_c),sK1) != mult(op_c,mult(sK0,sK1))
| spl2_2 ),
inference(forward_demodulation,[],[f30,f87]) ).
fof(f431,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f430,f133]) ).
fof(f432,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f431]) ).
fof(f434,plain,
( mult(mult(sK0,sK1),op_c) != mult(op_c,mult(sK0,sK1))
| spl2_3 ),
inference(forward_demodulation,[],[f34,f83]) ).
fof(f435,plain,
( $false
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f434,f21]) ).
fof(f436,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f435]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f408]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f432]) ).
cnf(s4,plain,
spl2_3,
inference(sat_conversion,[],[f436]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f437,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP665+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n005.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 10:33:32 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.46 Running first-order model finding
% 0.12/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.51 % (3794890)Will run a generic schedule for satisfiability detection.
% 0.21/0.51 % (3794899)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1882021498:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.51 % (3794895)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3539332345_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.51 % TRYING [1]
% 0.21/0.51 % TRYING [2]
% 0.21/0.51 % TRYING [3]
% 0.21/0.51 % (3794896)% WARNING: option uhcvi not known.
% 0.21/0.51 % (3794899) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3794890-3794899"...
% 0.21/0.51 % TRYING [4]
% 0.21/0.51 % (3794899)...printing done.
% 0.21/0.51 % (3794899)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (3794899)------------------------------
% 0.21/0.51 % (3794899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.51 % (3794899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.51 % (3794899)CaDiCaL version: 2.1.3
% 0.21/0.51 % (3794899)Termination reason: Refutation
% 0.21/0.51 % (3794899)Time elapsed: 0.011 s
% 0.21/0.51 % (3794899)Peak memory usage: 12 MB
% 0.21/0.51 % (3794899)Instructions burned: 18 (million)
% 0.21/0.51 % (3794890)Success in time 0.034 s
% 0.21/0.51 % Vampire exiting
%------------------------------------------------------------------------------