%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 12:25:56 PM UTC 2026
% Result : Theorem 0.16s 0.54s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 20 unt; 2 def)
% Number of atoms : 138 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 130 ( 60 ~; 56 |; 7 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 92 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd512)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(315), 516, 0)') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 1)') ).
fof(f6,axiom,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
fof(f17,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( less(X1,X2)
& less(X0,X1) )
=> less(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof(f41,axiom,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f42,axiom,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f43,axiom,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(f45,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f47,axiom,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : X0 = vplus(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f48,axiom,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : X1 = vplus(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f65,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(flattening,[],[f2]) ).
fof(f88,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f89,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(flattening,[],[f88]) ).
fof(f92,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f93,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f105,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X2] : X0 = vplus(X1,X2)
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f106,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X3] : vplus(X1,X3) = X0
| ~ less(X1,X0) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( vplus(X1,sK0(X0,X1)) = X0
| ~ less(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : X1 = vplus(X0,X2)
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f109,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f109]) ).
fof(f112,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(cnf_transformation,[],[f65]) ).
fof(f114,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(cnf_transformation,[],[f4]) ).
fof(f116,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(cnf_transformation,[],[f6]) ).
fof(f127,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f149,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f158,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f159,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f160,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| less(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f162,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f165,plain,
! [X2,X0,X1] :
( less(X1,X0)
| vplus(X1,X2) != X0 ),
inference(cnf_transformation,[],[f107]) ).
fof(f166,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| vplus(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f110]) ).
fof(f201,plain,
! [X2,X1] : less(X1,vplus(X1,X2)),
inference(equality_resolution,[],[f165]) ).
fof(f218,plain,
! [X2,X0,X1] :
( less(X1,X2)
| ~ less(X0,X2)
| less(X0,X1) ),
inference(consistent_polarity_flipping,[],[f149]) ).
fof(f226,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X1,X0) ),
inference(consistent_polarity_flipping,[],[f158]) ).
fof(f227,plain,
! [X0,X1] :
( ~ less(X1,X0)
| ~ greater(X0,X1) ),
inference(consistent_polarity_flipping,[],[f159]) ).
fof(f228,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f160]) ).
fof(f230,plain,
! [X0,X1] :
( less(X0,X1)
| ~ greater(X0,X1) ),
inference(consistent_polarity_flipping,[],[f162]) ).
fof(f231,plain,
! [X2,X1] : ~ less(X1,vplus(X1,X2)),
inference(consistent_polarity_flipping,[],[f201]) ).
fof(f241,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ greater(X1,X0) ),
inference(resolution,[],[f230,f227]) ).
fof(f254,plain,
greater(vmul(vd508,vd511),vmul(vd511,vd509)),
inference(superposition,[],[f116,f127]) ).
fof(f255,plain,
greater(vmul(vd511,vd509),vmul(vd509,vd512)),
inference(superposition,[],[f114,f127]) ).
fof(f404,plain,
! [X2,X0,X1] :
( ~ less(X0,vplus(X1,X2))
| less(X0,X1) ),
inference(resolution,[],[f218,f231]) ).
fof(f416,plain,
! [X2,X0,X1] :
( less(X0,X1)
| ~ greater(X0,vplus(X1,X2)) ),
inference(resolution,[],[f404,f230]) ).
fof(f520,plain,
! [X2,X0,X1] :
( ~ greater(X0,vplus(X1,X2))
| ~ greater(X1,X0) ),
inference(resolution,[],[f416,f227]) ).
fof(f605,plain,
! [X0,X1] :
( greater(X1,X0)
| X0 = X1
| greater(X0,X1) ),
inference(resolution,[],[f228,f226]) ).
fof(f643,plain,
( vmul(vd508,vd511) = vmul(vd509,vd512)
| greater(vmul(vd509,vd512),vmul(vd508,vd511)) ),
inference(resolution,[],[f605,f112]) ).
fof(f647,definition,
( spl4_1
<=> greater(vmul(vd509,vd512),vmul(vd508,vd511)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f649,plain,
( greater(vmul(vd509,vd512),vmul(vd508,vd511))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f651,definition,
( spl4_2
<=> vmul(vd508,vd511) = vmul(vd509,vd512) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f653,plain,
( vmul(vd508,vd511) = vmul(vd509,vd512)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f654,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f643,f651,f647]) ).
fof(f657,plain,
( greater(vmul(vd511,vd509),vmul(vd508,vd511))
| ~ spl4_2 ),
inference(superposition,[],[f255,f653]) ).
fof(f662,plain,
( ~ greater(vmul(vd508,vd511),vmul(vd511,vd509))
| ~ spl4_2 ),
inference(resolution,[],[f657,f241]) ).
fof(f663,plain,
( $false
| ~ spl4_2 ),
inference(resolution,[],[f662,f254]) ).
fof(f665,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f663]) ).
fof(f1680,plain,
( vmul(vd509,vd512) = vplus(vmul(vd508,vd511),sK1(vmul(vd508,vd511),vmul(vd509,vd512)))
| ~ spl4_1 ),
inference(resolution,[],[f166,f649]) ).
fof(f1755,plain,
( ! [X0] :
( ~ greater(X0,vmul(vd509,vd512))
| ~ greater(vmul(vd508,vd511),X0) )
| ~ spl4_1 ),
inference(superposition,[],[f520,f1680]) ).
fof(f1848,plain,
( ~ greater(vmul(vd508,vd511),vmul(vd511,vd509))
| ~ spl4_1 ),
inference(resolution,[],[f1755,f255]) ).
fof(f1857,plain,
( $false
| ~ spl4_1 ),
inference(resolution,[],[f1848,f254]) ).
fof(f1859,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f1857]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f654]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f665]) ).
cnf(s8,plain,
~ spl4_1,
inference(sat_conversion,[],[f1859]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s2,s8]) ).
fof(f1869,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n008.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 21:32:24 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.16/0.54 % (1621290)Will run a generic schedule for satisfiability detection.
% 0.16/0.54 % (1621299)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3394499385:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.54 % (1621296)% WARNING: option uhcvi not known.
% 0.16/0.54 % (1621295)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4276579582_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.54 % (1621296)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3561571944:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.54 % (1621297)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=881134954:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.54 % (1621300)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=279537491:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.54 % (1621298)dis+10_1_sil=32000:sp=arity:random_seed=4253156128:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.54 % (1621301)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4079568565:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.54 % TRYING [1]
% 0.16/0.54 % TRYING [2]
% 0.16/0.54 % TRYING [3]
% 0.16/0.54 % TRYING [4]
% 0.16/0.54 % (1621299)Instruction limit reached!
% 0.16/0.54 % (1621299)------------------------------
% 0.16/0.54 % (1621299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (1621299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (1621299)CaDiCaL version: 2.1.3
% 0.16/0.54 % (1621299)Termination reason: Instruction limit
% 0.16/0.54 % (1621299)Termination phase: Saturation
% 0.16/0.54 % (1621299)Time elapsed: 0.043 s
% 0.16/0.54 % (1621299)Peak memory usage: 13 MB
% 0.16/0.54 % (1621299)Instructions burned: 118 (million)
% 0.16/0.54 % TRYING [5]
% 0.16/0.54 % (1621309)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3384337658:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.54 % TRYING [1]
% 0.16/0.54 % TRYING [2]
% 0.16/0.54 % TRYING [3]
% 0.16/0.54 % TRYING [4]
% 0.16/0.54 % (1621301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1621290-1621301"...
% 0.16/0.54 % (1621298)Instruction limit reached!
% 0.16/0.54 % (1621298)------------------------------
% 0.16/0.54 % (1621298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (1621298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (1621298)CaDiCaL version: 2.1.3
% 0.16/0.54 % (1621298)Termination reason: Instruction limit
% 0.16/0.54 % (1621298)Termination phase: Saturation
% 0.16/0.54 % (1621298)Time elapsed: 0.067 s
% 0.16/0.54 % (1621298)Peak memory usage: 12 MB
% 0.16/0.54 % (1621298)Instructions burned: 104 (million)
% 0.16/0.54 % (1621296) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1621290-1621296"...
% 0.16/0.54 % (1621301)...printing done.
% 0.16/0.54 % (1621301)Refutation found. Thanks to Tanya!
% 0.16/0.54 % SZS status Theorem for theBenchmark
% 0.16/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.54 % (1621301)------------------------------
% 0.16/0.54 % (1621301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (1621301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (1621301)CaDiCaL version: 2.1.3
% 0.16/0.54 % (1621301)Termination reason: Refutation
% 0.16/0.54 % (1621301)Time elapsed: 0.067 s
% 0.16/0.54 % (1621301)Peak memory usage: 14 MB
% 0.16/0.54 % (1621301)Instructions burned: 119 (million)
% 0.16/0.54 % (1621290)Success in time 0.113 s
% 0.16/0.54 % Vampire exiting
%------------------------------------------------------------------------------