%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM853+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:17:16 PM UTC 2026
% Result : Theorem 3.46s 1.45s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 18 unt; 2 def)
% Number of atoms : 107 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 96 ( 44 ~; 39 |; 6 &)
% ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vd486,vd488),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(307), 490, 0)') ).
fof(f2,negated_conjecture,
~ greater(vd486,vd488),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(307), 489, 0)') ).
fof(f6,axiom,
! [X0,X1,X2] :
( greater(X1,X2)
=> greater(vmul(X1,X0),vmul(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
fof(f17,axiom,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f18,axiom,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f19,axiom,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(f20,axiom,
! [X0,X1] :
( X0 != X1
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f21,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f23,axiom,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : X0 = vplus(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f24,axiom,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : X1 = vplus(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f39,plain,
~ greater(vd486,vd488),
inference(flattening,[],[f2]) ).
fof(f43,plain,
! [X0,X1,X2] :
( greater(vmul(X1,X0),vmul(X2,X0))
| ~ greater(X1,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f55,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X2] : X0 = vplus(X1,X2)
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f56,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X3] : vplus(X1,X3) = X0
| ~ less(X1,X0) ) ),
inference(rectify,[],[f55]) ).
fof(f57,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))],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : X1 = vplus(X0,X2)
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f59,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f58]) ).
fof(f60,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))],[f59]) ).
fof(f62,plain,
~ greater(vd486,vd488),
inference(cnf_transformation,[],[f39]) ).
fof(f63,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(cnf_transformation,[],[f3]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| greater(vmul(X1,X0),vmul(X2,X0)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f77,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f78,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f79,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f80,plain,
! [X0,X1] :
( X0 != X1
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f81,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f84,plain,
! [X2,X0,X1] :
( less(X1,X0)
| vplus(X1,X2) != X0 ),
inference(cnf_transformation,[],[f57]) ).
fof(f85,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| vplus(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f103,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f80]) ).
fof(f105,plain,
! [X2,X1] : less(X1,vplus(X1,X2)),
inference(equality_resolution,[],[f84]) ).
fof(f111,plain,
less(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(resolution,[],[f63,f78]) ).
fof(f112,plain,
! [X0,X1] : ~ greater(X0,vplus(X0,X1)),
inference(resolution,[],[f105,f81]) ).
fof(f116,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| greater(X1,X0) ),
inference(resolution,[],[f79,f77]) ).
fof(f120,plain,
vmul(vd486,vd487) = vplus(vmul(vd488,vd487),sK1(vmul(vd488,vd487),vmul(vd486,vd487))),
inference(resolution,[],[f85,f63]) ).
fof(f225,plain,
( vd486 = vd488
| greater(vd488,vd486) ),
inference(resolution,[],[f116,f62]) ).
fof(f234,definition,
( spl4_1
<=> greater(vd488,vd486) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f236,plain,
( greater(vd488,vd486)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f238,definition,
( spl4_2
<=> vd486 = vd488 ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f240,plain,
( vd486 = vd488
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f241,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f225,f238,f234]) ).
fof(f242,plain,
( less(vmul(vd486,vd487),vmul(vd486,vd487))
| ~ spl4_2 ),
inference(superposition,[],[f111,f240]) ).
fof(f247,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f242,f103]) ).
fof(f248,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f268,plain,
( ! [X0] : greater(vmul(vd488,X0),vmul(vd486,X0))
| ~ spl4_1 ),
inference(resolution,[],[f236,f66]) ).
fof(f577,plain,
~ greater(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(superposition,[],[f112,f120]) ).
fof(f581,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f577,f268]) ).
fof(f582,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f581]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f241]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
~ spl4_1,
inference(sat_conversion,[],[f582]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f584,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM853+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 21:34:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.46/1.45 % (3425604)Detected formulas, will run a generic FOF schedule.
% 3.46/1.45 % (3425609)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=4034562027:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.45 % (3425613)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4278589826:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.45 % (3425612)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1681779403:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.45 % (3425611)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=3320156793:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.45 % (3425614)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=652796028:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.45 % (3425610)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=1920606788:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.45 % (3425612)Refutation not found, incomplete strategy
% 3.46/1.45 % (3425612)------------------------------
% 3.46/1.45 % (3425612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.45 % (3425612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.45 % (3425612)CaDiCaL version: 2.1.3
% 3.46/1.45 % (3425612)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.45 % (3425612)Time elapsed: 0.001 s
% 3.46/1.45 % (3425612)Peak memory usage: 88 MB
% 3.46/1.45 % (3425615)dis-21_1_sil=8000:lcm=predicate:random_seed=2806558156: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)
% 3.46/1.45 % (3425614)First to succeed.
% 3.46/1.45 % (3425614)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3425604"
% 3.46/1.45 % (3425613)Instruction limit reached!
% 3.46/1.45 % (3425613)------------------------------
% 3.46/1.45 % (3425613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.45 % (3425613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.45 % (3425613)CaDiCaL version: 2.1.3
% 3.46/1.45 % (3425613)Termination reason: Instruction limit
% 3.46/1.45 % (3425613)Termination phase: Saturation
% 3.46/1.45 % (3425613)Time elapsed: 0.067 s
% 3.46/1.45 % (3425613)Peak memory usage: 89 MB
% 3.46/1.45 % (3425613)Instructions burned: 120 (million)
% 3.46/1.45 % (3425615)Instruction limit reached!
% 3.46/1.45 % (3425615)------------------------------
% 3.46/1.45 % (3425615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.45 % (3425615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.45 % (3425615)CaDiCaL version: 2.1.3
% 3.46/1.45 % (3425615)Termination reason: Instruction limit
% 3.46/1.45 % (3425615)Termination phase: Saturation
% 3.46/1.45 % (3425615)Time elapsed: 0.081 s
% 3.46/1.45 % (3425615)Peak memory usage: 88 MB
% 3.46/1.45 % (3425615)Instructions burned: 129 (million)
% 3.46/1.45 % (3425623)lrs+10_1_sil=8000:sp=occurrence:random_seed=3222581309:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.46/1.45 % (3425624)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3041958469:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.46/1.45 % (3425612)------------------------------
% 3.46/1.45 % (3425612)------------------------------
% 3.46/1.45 % (3425614)Refutation found. Thanks to Tanya!
% 3.46/1.45 % SZS status Theorem for theBenchmark
% 3.46/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.45 % (3425614)------------------------------
% 3.46/1.45 % (3425614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.45 % (3425614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.45 % (3425614)CaDiCaL version: 2.1.3
% 3.46/1.45 % (3425614)Termination reason: Refutation
% 3.46/1.45 % (3425614)Time elapsed: 0.014 s
% 3.46/1.45 % (3425614)Peak memory usage: 90 MB
% 3.46/1.45 % (3425614)Instructions burned: 19 (million)
% 3.46/1.45 % (3425614)------------------------------
% 3.46/1.45 % (3425614)------------------------------
% 3.46/1.45 % (3425604)Success in time 0.407 s
% 3.46/1.45 % Vampire exiting
%------------------------------------------------------------------------------