%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM853+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 4.01s 1.53s
% Output : Refutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 17 unt; 2 def)
% Number of atoms : 100 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 42 ~; 37 |; 6 &)
% ( 4 <=>; 2 =>; 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 : 68 ( 0 sgn 62 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vd486,vd488),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
fof(f33,axiom,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f35,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(f37,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f38,axiom,
! [X0,X1] :
( X0 != X1
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f39,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(f40,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(f57,plain,
~ greater(vd486,vd488),
inference(flattening,[],[f2]) ).
fof(f60,plain,
! [X0,X1,X2] :
( greater(vmul(X1,X0),vmul(X2,X0))
| ~ greater(X1,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f81,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f94,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X2] : X0 = vplus(X1,X2)
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f95,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X3] : vplus(X1,X3) = X0
| ~ less(X1,X0) ) ),
inference(rectify,[],[f94]) ).
fof(f96,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))],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : X1 = vplus(X0,X2)
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f98,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f97]) ).
fof(f99,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))],[f98]) ).
fof(f101,plain,
~ greater(vd486,vd488),
inference(cnf_transformation,[],[f57]) ).
fof(f102,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(cnf_transformation,[],[f3]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| greater(vmul(X1,X0),vmul(X2,X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f139,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f141,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f143,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f144,plain,
! [X0,X1] :
( X0 != X1
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f146,plain,
! [X2,X0,X1] :
( less(X1,X0)
| vplus(X1,X2) != X0 ),
inference(cnf_transformation,[],[f96]) ).
fof(f147,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| vplus(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f171,plain,
! [X1] : ~ greater(X1,X1),
inference(equality_resolution,[],[f144]) ).
fof(f172,plain,
! [X2,X1] : less(X1,vplus(X1,X2)),
inference(equality_resolution,[],[f146]) ).
fof(f187,definition,
( spl4_2
<=> vd486 = vd488 ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f189,plain,
( vd486 = vd488
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f194,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| greater(X1,X0) ),
inference(resolution,[],[f141,f139]) ).
fof(f195,plain,
! [X0,X1] : ~ greater(X0,vplus(X0,X1)),
inference(resolution,[],[f172,f143]) ).
fof(f206,plain,
vmul(vd486,vd487) = vplus(vmul(vd488,vd487),sK1(vmul(vd488,vd487),vmul(vd486,vd487))),
inference(resolution,[],[f147,f102]) ).
fof(f411,plain,
( vd486 = vd488
| greater(vd488,vd486) ),
inference(resolution,[],[f194,f101]) ).
fof(f415,definition,
( spl4_3
<=> greater(vd488,vd486) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f417,plain,
( greater(vd488,vd486)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f418,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f411,f187,f415]) ).
fof(f419,plain,
( ! [X0] : greater(vmul(vd488,X0),vmul(vd486,X0))
| ~ spl4_3 ),
inference(resolution,[],[f417,f105]) ).
fof(f1293,plain,
~ greater(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(superposition,[],[f195,f206]) ).
fof(f1303,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1293,f419]) ).
fof(f1304,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f1303]) ).
fof(f1307,plain,
( greater(vmul(vd486,vd487),vmul(vd486,vd487))
| ~ spl4_2 ),
inference(superposition,[],[f102,f189]) ).
fof(f1326,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f1307,f171]) ).
fof(f1327,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f1326]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f418]) ).
cnf(s5,plain,
~ spl4_3,
inference(sat_conversion,[],[f1304]) ).
cnf(s12,plain,
~ spl4_2,
inference(sat_conversion,[],[f1327]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s2,s5,s12]) ).
fof(f1328,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM853+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.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 21:39:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.53 % (3014410)Detected formulas, will run a generic FOF schedule.
% 4.01/1.53 % (3014417)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=477132886:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.01/1.53 % (3014419)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1338727085:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.01/1.53 % (3014418)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1357688863:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.01/1.53 % (3014418)Refutation not found, incomplete strategy
% 4.01/1.53 % (3014418)------------------------------
% 4.01/1.53 % (3014418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.53 % (3014418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.53 % (3014418)CaDiCaL version: 2.1.3
% 4.01/1.53 % (3014418)Termination reason: Refutation not found, incomplete strategy
% 4.01/1.53 % (3014418)Time elapsed: 0.001 s
% 4.01/1.53 % (3014418)Peak memory usage: 88 MB
% 4.01/1.53 % (3014415)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=2456490889:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.01/1.53 % (3014416)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=1290609067:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.01/1.53 % (3014421)dis-21_1_sil=8000:lcm=predicate:random_seed=12143669: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)
% 4.01/1.53 % (3014420)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1474677473:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.01/1.53 % (3014420)First to succeed.
% 4.01/1.53 % (3014420)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3014410"
% 4.01/1.53 % (3014419)Instruction limit reached!
% 4.01/1.53 % (3014419)------------------------------
% 4.01/1.53 % (3014419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.53 % (3014419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.53 % (3014419)CaDiCaL version: 2.1.3
% 4.01/1.53 % (3014419)Termination reason: Instruction limit
% 4.01/1.53 % (3014419)Termination phase: Saturation
% 4.01/1.53 % (3014419)Time elapsed: 0.069 s
% 4.01/1.53 % (3014419)Peak memory usage: 88 MB
% 4.01/1.53 % (3014419)Instructions burned: 119 (million)
% 4.01/1.53 % (3014421)Instruction limit reached!
% 4.01/1.53 % (3014421)------------------------------
% 4.01/1.53 % (3014421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.53 % (3014421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.53 % (3014421)CaDiCaL version: 2.1.3
% 4.01/1.53 % (3014421)Termination reason: Instruction limit
% 4.01/1.53 % (3014421)Termination phase: Saturation
% 4.01/1.53 % (3014421)Time elapsed: 0.079 s
% 4.01/1.53 % (3014421)Peak memory usage: 89 MB
% 4.01/1.53 % (3014421)Instructions burned: 129 (million)
% 4.01/1.53 % (3014429)lrs+10_1_sil=8000:sp=occurrence:random_seed=2003342976:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.01/1.53 % (3014418)------------------------------
% 4.01/1.53 % (3014418)------------------------------
% 4.01/1.53 % (3014429)Also succeeded, but the first one will report.
% 4.01/1.53 % (3014430)lrs+10_1_sil=32000:urr=on:br=off:random_seed=508595245:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.01/1.53 % (3014420)Refutation found. Thanks to Tanya!
% 4.01/1.53 % SZS status Theorem for theBenchmark
% 4.01/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 4.01/1.53 % (3014420)------------------------------
% 4.01/1.53 % (3014420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.53 % (3014420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.53 % (3014420)CaDiCaL version: 2.1.3
% 4.01/1.53 % (3014420)Termination reason: Refutation
% 4.01/1.53 % (3014420)Time elapsed: 0.031 s
% 4.01/1.53 % (3014420)Peak memory usage: 90 MB
% 4.01/1.53 % (3014420)Instructions burned: 40 (million)
% 4.01/1.53 % (3014420)------------------------------
% 4.01/1.53 % (3014420)------------------------------
% 4.01/1.53 % (3014410)Success in time 0.477 s
% 4.01/1.53 % Vampire exiting
%------------------------------------------------------------------------------