%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP711+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 : n012.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 10:18:38 AM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 29 unt; 3 def)
% Number of atoms : 135 ( 77 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 107 ( 49 ~; 45 |; 6 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 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 : 74 ( 0 sgn 71 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1,X2] : mult(X2,mult(X1,mult(X1,X0))) = mult(mult(mult(X2,X1),X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0] : mult(X0,i(X0)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X0] : mult(i(X0),X0) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( ( mult(X0,X1) = mult(X0,X2)
=> X1 = X2 )
& ( mult(X1,X0) = mult(X2,X0)
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( ( mult(X0,X1) = mult(X0,X2)
=> X1 = X2 )
& ( mult(X1,X0) = mult(X2,X0)
=> X1 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
? [X0,X1,X2] :
( ( X1 != X2
& mult(X0,X1) = mult(X0,X2) )
| ( X1 != X2
& mult(X1,X0) = mult(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
( ( sK1 != sK2
& mult(sK0,sK1) = mult(sK0,sK2) )
| ( sK1 != sK2
& mult(sK1,sK0) = mult(sK2,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
fof(f10,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X2,X0,X1] : mult(X2,mult(X1,mult(X1,X0))) = mult(mult(mult(X2,X1),X1),X0),
inference(cnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0] : unit = mult(X0,i(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f14,plain,
! [X0] : unit = mult(i(X0),X0),
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
( mult(sK0,sK1) = mult(sK0,sK2)
| mult(sK1,sK0) = mult(sK2,sK0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
( sK1 != sK2
| sK1 != sK2 ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
sK1 != sK2,
inference(duplicate_literal_removal,[],[f18]) ).
fof(f21,definition,
( spl3_1
<=> mult(sK1,sK0) = mult(sK2,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f23,plain,
( mult(sK1,sK0) = mult(sK2,sK0)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,definition,
( spl3_2
<=> mult(sK0,sK1) = mult(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f27,plain,
( mult(sK0,sK1) = mult(sK0,sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f15,f25,f21]) ).
fof(f30,definition,
( spl3_3
<=> sK1 = sK2 ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f32,plain,
( sK1 != sK2
| spl3_3 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f35,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f19,f30]) ).
fof(f43,plain,
! [X0,X1] : mult(X0,mult(i(X0),mult(i(X0),X1))) = mult(mult(unit,i(X0)),X1),
inference(superposition,[],[f12,f13]) ).
fof(f44,plain,
! [X0,X1] : mult(unit,mult(X0,mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(superposition,[],[f12,f11]) ).
fof(f45,plain,
! [X2,X3,X0,X1] : mult(mult(mult(X0,X1),X1),mult(X2,mult(X2,X3))) = mult(mult(mult(X0,mult(X1,mult(X1,X2))),X2),X3),
inference(superposition,[],[f12,f12]) ).
fof(f46,plain,
! [X0,X1] : mult(i(X0),mult(X0,mult(X0,X1))) = mult(mult(unit,X0),X1),
inference(superposition,[],[f12,f14]) ).
fof(f47,plain,
( ! [X0] : mult(sK0,mult(sK2,mult(sK2,X0))) = mult(mult(mult(sK0,sK1),sK2),X0)
| ~ spl3_2 ),
inference(superposition,[],[f12,f27]) ).
fof(f51,plain,
! [X0,X1] : unit = mult(X0,mult(X1,mult(X1,i(mult(mult(X0,X1),X1))))),
inference(superposition,[],[f12,f13]) ).
fof(f52,plain,
! [X0,X1] : mult(mult(X0,X1),X1) = mult(X0,mult(X1,mult(X1,unit))),
inference(superposition,[],[f10,f12]) ).
fof(f54,plain,
! [X0,X1] : mult(mult(X0,X1),X1) = mult(X0,mult(X1,X1)),
inference(forward_demodulation,[],[f52,f10]) ).
fof(f57,plain,
! [X0,X1] : mult(X0,X1) = mult(i(X0),mult(X0,mult(X0,X1))),
inference(forward_demodulation,[],[f46,f11]) ).
fof(f58,plain,
! [X2,X3,X0,X1] : mult(mult(mult(X0,mult(X1,mult(X1,X2))),X2),X3) = mult(X0,mult(X1,mult(X1,mult(X2,mult(X2,X3))))),
inference(forward_demodulation,[],[f45,f12]) ).
fof(f59,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(forward_demodulation,[],[f44,f11]) ).
fof(f60,plain,
! [X0,X1] : mult(i(X0),X1) = mult(X0,mult(i(X0),mult(i(X0),X1))),
inference(forward_demodulation,[],[f43,f11]) ).
fof(f67,plain,
( mult(mult(sK0,sK1),sK2) = mult(sK0,mult(sK2,mult(sK2,unit)))
| ~ spl3_2 ),
inference(superposition,[],[f10,f47]) ).
fof(f71,plain,
( mult(mult(sK0,sK1),sK2) = mult(sK0,mult(sK2,sK2))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f67,f10]) ).
fof(f73,plain,
( ! [X0] : mult(sK0,mult(sK2,mult(sK2,X0))) = mult(mult(sK0,mult(sK2,sK2)),X0)
| ~ spl3_2 ),
inference(superposition,[],[f47,f71]) ).
fof(f135,plain,
( ! [X0] : mult(mult(mult(sK0,sK1),sK2),X0) = mult(i(mult(mult(sK0,sK1),sK2)),mult(sK0,mult(sK2,mult(sK2,mult(mult(mult(sK0,sK1),sK2),X0)))))
| ~ spl3_2 ),
inference(superposition,[],[f57,f47]) ).
fof(f140,plain,
( ! [X0] : mult(sK0,mult(sK2,mult(sK2,X0))) = mult(i(mult(mult(sK0,sK1),sK2)),mult(sK0,mult(sK2,mult(sK2,mult(sK0,mult(sK2,mult(sK2,X0)))))))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f135,f47]) ).
fof(f151,plain,
( ! [X0] : mult(sK0,mult(sK2,mult(sK2,X0))) = mult(i(mult(sK0,mult(sK2,sK2))),mult(sK0,mult(sK2,mult(sK2,mult(sK0,mult(sK2,mult(sK2,X0)))))))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f140,f71]) ).
fof(f163,plain,
! [X0,X1] : unit = mult(X0,mult(X1,mult(X1,i(mult(X0,mult(X1,X1)))))),
inference(forward_demodulation,[],[f51,f54]) ).
fof(f1194,plain,
( mult(sK0,unit) = mult(i(mult(sK0,mult(sK2,sK2))),mult(sK0,mult(sK2,mult(sK2,mult(sK0,unit)))))
| ~ spl3_2 ),
inference(superposition,[],[f151,f163]) ).
fof(f1208,plain,
( sK0 = mult(i(mult(sK0,mult(sK2,sK2))),mult(sK0,mult(sK2,mult(sK2,sK0))))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1194,f10]) ).
fof(f1213,plain,
( sK0 = mult(mult(sK0,mult(sK2,sK2)),mult(i(mult(sK0,mult(sK2,sK2))),sK0))
| ~ spl3_2 ),
inference(superposition,[],[f60,f1208]) ).
fof(f1218,plain,
( sK0 = mult(sK0,mult(sK2,mult(sK2,mult(i(mult(sK0,mult(sK2,sK2))),sK0))))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1213,f73]) ).
fof(f1223,plain,
( sK0 = mult(i(sK0),mult(sK0,sK0))
| ~ spl3_2 ),
inference(superposition,[],[f57,f1218]) ).
fof(f1259,plain,
( ! [X0,X1] : mult(X0,mult(i(sK0),mult(i(sK0),mult(mult(sK0,sK0),mult(mult(sK0,sK0),X1))))) = mult(mult(mult(X0,mult(i(sK0),sK0)),mult(sK0,sK0)),X1)
| ~ spl3_2 ),
inference(superposition,[],[f58,f1223]) ).
fof(f1266,plain,
( ! [X0,X1] : mult(X0,mult(i(sK0),mult(i(sK0),mult(mult(sK0,sK0),mult(mult(sK0,sK0),X1))))) = mult(mult(mult(X0,unit),mult(sK0,sK0)),X1)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1259,f14]) ).
fof(f1271,plain,
( ! [X0,X1] : mult(X0,mult(i(sK0),mult(i(sK0),mult(mult(sK0,sK0),mult(mult(sK0,sK0),X1))))) = mult(mult(X0,mult(sK0,sK0)),X1)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1266,f10]) ).
fof(f1273,plain,
( ! [X0,X1] : mult(mult(X0,mult(sK0,sK0)),X1) = mult(X0,mult(i(sK0),mult(i(sK0),mult(sK0,mult(sK0,mult(mult(sK0,sK0),X1))))))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1271,f59]) ).
fof(f1274,plain,
( ! [X0,X1] : mult(mult(X0,mult(sK0,sK0)),X1) = mult(X0,mult(i(sK0),mult(sK0,mult(mult(sK0,sK0),X1))))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1273,f57]) ).
fof(f1275,plain,
( ! [X0,X1] : mult(mult(X0,mult(sK0,sK0)),X1) = mult(X0,mult(i(sK0),mult(sK0,mult(sK0,mult(sK0,X1)))))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1274,f59]) ).
fof(f1276,plain,
( ! [X0,X1] : mult(mult(X0,mult(sK0,sK0)),X1) = mult(X0,mult(sK0,mult(sK0,X1)))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1275,f57]) ).
fof(f1482,plain,
( ! [X0] : mult(unit,X0) = mult(i(mult(sK0,sK0)),mult(sK0,mult(sK0,X0)))
| ~ spl3_2 ),
inference(superposition,[],[f1276,f14]) ).
fof(f1558,plain,
( ! [X0] : mult(i(mult(sK0,sK0)),mult(sK0,mult(sK0,X0))) = X0
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1482,f11]) ).
fof(f1601,plain,
( sK2 = mult(i(mult(sK0,sK0)),mult(sK0,mult(sK0,sK1)))
| ~ spl3_2 ),
inference(superposition,[],[f1558,f27]) ).
fof(f1640,plain,
( sK1 = sK2
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1601,f1558]) ).
fof(f1641,plain,
( $false
| ~ spl3_2
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f1640,f32]) ).
fof(f1642,plain,
( ~ spl3_2
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f1641]) ).
fof(f1646,plain,
( ! [X0] : mult(sK2,mult(sK0,mult(sK0,X0))) = mult(mult(mult(sK1,sK0),sK0),X0)
| ~ spl3_1 ),
inference(superposition,[],[f12,f23]) ).
fof(f1647,plain,
( ! [X0] : mult(sK2,mult(sK0,mult(sK0,X0))) = mult(sK1,mult(sK0,mult(sK0,X0)))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1646,f12]) ).
fof(f1653,plain,
( mult(sK2,unit) = mult(sK1,unit)
| ~ spl3_1 ),
inference(superposition,[],[f1647,f163]) ).
fof(f1666,plain,
( sK1 = mult(sK2,unit)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1653,f10]) ).
fof(f1669,plain,
( sK1 = sK2
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1666,f10]) ).
fof(f1670,plain,
( $false
| ~ spl3_1
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f1669,f32]) ).
fof(f1671,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f1670]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
~ spl3_3,
inference(sat_conversion,[],[f35]) ).
cnf(s5,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f1642]) ).
cnf(s6,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f1671]) ).
cnf(s7,plain,
~ spl3_1,
inference(rat,[],[s6,s4]) ).
cnf(s8,plain,
~ spl3_2,
inference(rat,[],[s5,s4]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s7]) ).
fof(f1672,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP711+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.34 % Computer : n012.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 27 10:36:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 Running first-order model finding
% 0.09/0.36 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
% 0.09/0.42 % (2184562)Will run a generic schedule for satisfiability detection.
% 0.09/0.42 % (2184570)% WARNING: option uhcvi not known.
% 0.09/0.42 % (2184573)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3899856718:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.42 % (2184569)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2544758562_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.42 % (2184572)dis+10_1_sil=32000:sp=arity:random_seed=218252489:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.42 % (2184570)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2231840673:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.42 % (2184575)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2841217851:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.42 % (2184571)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=421828102:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.42 % (2184574)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3528517348:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.42 % TRYING [1]
% 0.09/0.42 % TRYING [2]
% 0.09/0.42 % TRYING [3]
% 0.09/0.42 % TRYING [4]
% 0.09/0.42 % TRYING [5]
% 0.09/0.42 % TRYING [6]
% 0.09/0.42 % (2184572) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2184562-2184572"...
% 0.09/0.42 % (2184572)...printing done.
% 0.09/0.42 % (2184572)Refutation found. Thanks to Tanya!
% 0.09/0.42 % SZS status Theorem for theBenchmark
% 0.09/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.42 % (2184572)------------------------------
% 0.09/0.42 % (2184572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.42 % (2184572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.42 % (2184572)CaDiCaL version: 2.1.3
% 0.09/0.42 % (2184572)Termination reason: Refutation
% 0.09/0.42 % (2184572)Time elapsed: 0.029 s
% 0.09/0.42 % (2184572)Peak memory usage: 13 MB
% 0.09/0.42 % (2184572)Instructions burned: 105 (million)
% 0.09/0.42 % (2184562)Success in time 0.057 s
% 0.09/0.42 % Vampire exiting
%------------------------------------------------------------------------------