%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD069-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 09:49:20 AM UTC 2026
% Result : Unsatisfiable 3.60s 1.28s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 36 ( 13 unt; 2 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 33 ~; 31 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f16,axiom,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f19,axiom,
! [X2,X0,X1] :
( less_or_equal(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ less_or_equal(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f22,axiom,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1)
| ~ equalish(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
fof(f29,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f31,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f32,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_equal_to_additive_identity_5) ).
fof(f33,negated_conjecture,
equalish(add(a,b),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_additive_identity_6) ).
fof(f34,plain,
equalish(additive_identity,add(a,b)),
inference(resolution,[],[f22,f33]) ).
fof(f58,plain,
! [X0] :
( ~ equalish(X0,add(a,b))
| equalish(X0,additive_identity) ),
inference(resolution,[],[f23,f33]) ).
fof(f63,plain,
! [X0] :
( ~ equalish(additive_identity,X0)
| less_or_equal(X0,b) ),
inference(resolution,[],[f26,f31]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ~ equalish(add(X1,X0),X3)
| ~ less_or_equal(X1,X2)
| less_or_equal(X3,add(X2,X0))
| ~ defined(X0) ),
inference(resolution,[],[f19,f26]) ).
fof(f142,plain,
less_or_equal(add(a,b),b),
inference(resolution,[],[f63,f34]) ).
fof(f152,plain,
( ~ less_or_equal(b,add(a,b))
| equalish(b,add(a,b)) ),
inference(resolution,[],[f142,f16]) ).
fof(f154,definition,
( spl0_9
<=> equalish(b,add(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f156,plain,
( equalish(b,add(a,b))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f158,definition,
( spl0_10
<=> less_or_equal(b,add(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f160,plain,
( ~ less_or_equal(b,add(a,b))
| spl0_10 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f152,f158,f154]) ).
fof(f468,plain,
! [X0,X1] :
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(X1,add(X0,X1))
| ~ defined(X1)
| ~ defined(X1) ),
inference(resolution,[],[f135,f2]) ).
fof(f482,plain,
! [X0,X1] :
( less_or_equal(X1,add(X0,X1))
| ~ less_or_equal(additive_identity,X0)
| ~ defined(X1) ),
inference(duplicate_literal_removal,[],[f468]) ).
fof(f1270,plain,
( ~ less_or_equal(additive_identity,a)
| ~ defined(b)
| spl0_10 ),
inference(resolution,[],[f482,f160]) ).
fof(f1272,plain,
( ~ defined(b)
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f1270,f30]) ).
fof(f1274,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f1272,f29]) ).
fof(f1275,plain,
spl0_10,
inference(avatar_contradiction_clause,[],[f1274]) ).
fof(f1278,plain,
( equalish(b,additive_identity)
| ~ spl0_9 ),
inference(resolution,[],[f156,f58]) ).
fof(f1287,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f1278,f32]) ).
fof(f1288,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f1287]) ).
cnf(s5,plain,
( spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f161]) ).
cnf(s42,plain,
spl0_10,
inference(sat_conversion,[],[f1275]) ).
cnf(s44,plain,
~ spl0_9,
inference(sat_conversion,[],[f1288]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s5,s42,s44]) ).
fof(f1291,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD069-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 00:48:07 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 3.60/1.28 % (1756844)Input is clausal, will run a generic CNF schedule.
% 3.60/1.28 % (1756941)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1397261220:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.60/1.28 % (1756942)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4242230101:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.60/1.28 % (1756945)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1217781006:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.60/1.28 % (1756943)lrs+10_1_sil=8000:sp=occurrence:random_seed=1785924582:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.60/1.28 % (1756940)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=2191764847:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.60/1.28 % (1756946)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3975360143:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.60/1.28 % (1756947)dis-21_1_sil=8000:lcm=predicate:random_seed=1317117328:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.60/1.28 % (1756943)First to succeed.
% 3.60/1.28 % (1756943)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1756844"
% 3.60/1.28 % (1756947)Also succeeded, but the first one will report.
% 3.60/1.28 % (1756945)Instruction limit reached!
% 3.60/1.28 % (1756945)------------------------------
% 3.60/1.28 % (1756945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.28 % (1756945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.28 % (1756945)CaDiCaL version: 2.1.3
% 3.60/1.28 % (1756945)Termination reason: Instruction limit
% 3.60/1.28 % (1756945)Termination phase: Saturation
% 3.60/1.28 % (1756945)Time elapsed: 0.067 s
% 3.60/1.28 % (1756945)Peak memory usage: 88 MB
% 3.60/1.28 % (1756945)Instructions burned: 115 (million)
% 3.60/1.28 % (1756946)Also succeeded, but the first one will report.
% 3.60/1.28 % (1756960)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=691776204:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.60/1.28 % (1756943)Refutation found. Thanks to Tanya!
% 3.60/1.28 % SZS status Unsatisfiable for theBenchmark
% 3.60/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.28 % (1756943)------------------------------
% 3.60/1.28 % (1756943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.28 % (1756943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.28 % (1756943)CaDiCaL version: 2.1.3
% 3.60/1.28 % (1756943)Termination reason: Refutation
% 3.60/1.28 % (1756943)Time elapsed: 0.026 s
% 3.60/1.28 % (1756943)Peak memory usage: 89 MB
% 3.60/1.28 % (1756943)Instructions burned: 36 (million)
% 3.60/1.28 % (1756943)------------------------------
% 3.60/1.28 % (1756943)------------------------------
% 3.60/1.28 % (1756844)Success in time 0.416 s
% 3.60/1.28 % Vampire exiting
%------------------------------------------------------------------------------