%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM836+2 : 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 : n015.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 12:17:12 PM UTC 2026
% Result : Theorem 3.45s 1.43s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 11 unt; 1 def)
% Number of atoms : 57 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 28 ~; 18 |; 4 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 37 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ~ greater(vd203,vd204)
| ~ less(vd203,vd204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(ex(cond(conseq(131), 0), 1))') ).
fof(f2,negated_conjecture,
~ ( ~ greater(vd203,vd204)
| ~ less(vd203,vd204) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,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(f5,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(f8,axiom,
! [X0,X1] :
( ~ ? [X2] : X0 = vplus(X1,X2)
| ~ ? [X3] : X1 = vplus(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f13,plain,
! [X0,X1] :
( less(X1,X0)
=> ? [X2] : X0 = vplus(X1,X2) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f14,plain,
( greater(vd203,vd204)
& less(vd203,vd204) ),
inference(ennf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( ? [X2] : X0 = vplus(X1,X2)
| ~ less(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ! [X2] : vplus(X1,X2) != X0
| ! [X3] : vplus(X0,X3) != X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0,X1] :
( vplus(X1,sK0(X0,X1)) = X0
| ~ less(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f15]) ).
fof(f21,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : X1 = vplus(X0,X2)
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f25,plain,
less(vd203,vd204),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
greater(vd203,vd204),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ~ less(X1,X0)
| vplus(X1,sK0(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| vplus(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( vplus(X1,X2) != X0
| vplus(X0,X3) != X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
! [X2,X3,X1] : vplus(vplus(X1,X2),X3) != X1,
inference(equality_resolution,[],[f33]) ).
fof(f44,definition,
( spl4_1
<=> greater(vd203,vd204) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f45,plain,
( greater(vd203,vd204)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f52,plain,
spl4_1,
inference(avatar_split_clause,[],[f26,f44]) ).
fof(f53,plain,
vd204 = vplus(vd203,sK0(vd204,vd203)),
inference(resolution,[],[f28,f25]) ).
fof(f56,plain,
( vd203 = vplus(vd204,sK1(vd204,vd203))
| ~ spl4_1 ),
inference(resolution,[],[f29,f45]) ).
fof(f63,plain,
! [X0] : vd203 != vplus(vd204,X0),
inference(superposition,[],[f41,f53]) ).
fof(f68,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f56,f63]) ).
fof(f69,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f68]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f69]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f70,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM836+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n015.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 27 21:32:16 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 3.45/1.43 % (2022938)Detected formulas, will run a generic FOF schedule.
% 3.45/1.43 % (2022944)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=158072513:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.45/1.43 % (2022943)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=4150603237:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.45/1.43 % (2022946)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=124533519:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.45/1.43 % (2022945)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=3032044112:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.45/1.43 % (2022947)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3818058877:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.45/1.43 % (2022948)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2147177209:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.45/1.43 % (2022949)dis-21_1_sil=8000:lcm=predicate:random_seed=93135954: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)
% 3.45/1.43 % (2022946)Refutation not found, incomplete strategy
% 3.45/1.43 % (2022946)------------------------------
% 3.45/1.43 % (2022946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.43 % (2022946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.43 % (2022946)CaDiCaL version: 2.1.3
% 3.45/1.43 % (2022946)Termination reason: Refutation not found, incomplete strategy
% 3.45/1.43 % (2022946)Time elapsed: 0.001 s
% 3.45/1.43 % (2022946)Peak memory usage: 88 MB
% 3.45/1.43 % (2022949)Refutation not found, incomplete strategy
% 3.45/1.43 % (2022949)------------------------------
% 3.45/1.43 % (2022949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.43 % (2022949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.43 % (2022949)CaDiCaL version: 2.1.3
% 3.45/1.43 % (2022949)Termination reason: Refutation not found, incomplete strategy
% 3.45/1.43 % (2022949)Time elapsed: 0.002 s
% 3.45/1.43 % (2022949)Peak memory usage: 88 MB
% 3.45/1.43 % (2022949)Instructions burned: 2 (million)
% 3.45/1.43 % (2022948)First to succeed.
% 3.45/1.43 % (2022947)Also succeeded, but the first one will report.
% 3.45/1.43 % (2022948)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2022938"
% 3.45/1.43 % (2022949)------------------------------
% 3.45/1.43 % (2022949)------------------------------
% 3.45/1.43 % (2022946)------------------------------
% 3.45/1.43 % (2022946)------------------------------
% 3.45/1.43 % (2022948)Refutation found. Thanks to Tanya!
% 3.45/1.43 % SZS status Theorem for theBenchmark
% 3.45/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.43 % (2022948)------------------------------
% 3.45/1.43 % (2022948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.43 % (2022948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.43 % (2022948)CaDiCaL version: 2.1.3
% 3.45/1.43 % (2022948)Termination reason: Refutation
% 3.45/1.43 % (2022948)Time elapsed: 0.003 s
% 3.45/1.43 % (2022948)Peak memory usage: 90 MB
% 3.45/1.43 % (2022948)Instructions burned: 2 (million)
% 3.45/1.43 % (2022948)------------------------------
% 3.45/1.43 % (2022948)------------------------------
% 3.45/1.43 % (2022938)Success in time 0.405 s
% 3.45/1.43 % Vampire exiting
%------------------------------------------------------------------------------