%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD064-3 : 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 : 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 09:49:18 AM UTC 2026
% Result : Unsatisfiable 2.93s 1.18s
% Output : Refutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 10 unt; 3 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 169 ( 86 ~; 80 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X0)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f21,axiom,
! [X0,X1] :
( sum(additive_identity,X0,X1)
| ~ less_or_equal(X0,X1)
| ~ less_or_equal(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f23,axiom,
! [X0,X1] :
( less_or_equal(X1,X0)
| less_or_equal(X0,X1)
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X4] :
( ~ sum(X3,X4,X1)
| ~ less_or_equal(X2,X3)
| ~ sum(X2,X4,X0)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_2) ).
fof(f29,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_3) ).
fof(f35,plain,
( less_or_equal(additive_identity,additive_inverse(a))
| ~ defined(additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[],[f23,f29]) ).
fof(f39,definition,
( spl0_1
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f40,plain,
( ~ defined(additive_inverse(a))
| spl0_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f49,plain,
( less_or_equal(additive_identity,additive_inverse(a))
| ~ defined(additive_inverse(a)) ),
inference(forward_subsumption_resolution,[],[f35,f14]) ).
fof(f51,definition,
( spl0_4
<=> less_or_equal(additive_identity,additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f52,plain,
( less_or_equal(additive_identity,additive_inverse(a))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f49,f51,f39]) ).
fof(f54,plain,
( ~ defined(a)
| spl0_1 ),
inference(resolution,[],[f40,f15]) ).
fof(f55,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f54,f27]) ).
fof(f56,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ less_or_equal(X0,additive_inverse(X1))
| ~ sum(X0,X1,X2)
| less_or_equal(X2,additive_identity)
| ~ defined(X1) ),
inference(resolution,[],[f24,f4]) ).
fof(f174,plain,
( ! [X0] :
( ~ sum(additive_identity,a,X0)
| less_or_equal(X0,additive_identity)
| ~ defined(a) )
| ~ spl0_4 ),
inference(resolution,[],[f60,f52]) ).
fof(f188,plain,
( ! [X0] :
( ~ sum(additive_identity,a,X0)
| less_or_equal(X0,additive_identity) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f174,f27]) ).
fof(f189,plain,
( less_or_equal(a,additive_identity)
| ~ defined(a)
| ~ spl0_4 ),
inference(resolution,[],[f188,f3]) ).
fof(f191,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(X2,a,X3)
| ~ sum(X1,X2,additive_identity)
| less_or_equal(X0,additive_identity)
| ~ sum(X1,X3,X0) )
| ~ spl0_4 ),
inference(resolution,[],[f188,f2]) ).
fof(f194,plain,
( less_or_equal(a,additive_identity)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f189,f27]) ).
fof(f525,plain,
( ! [X2,X3,X0,X1] :
( ~ sum(a,X1,X3)
| less_or_equal(X2,additive_identity)
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,additive_identity) )
| ~ spl0_4 ),
inference(resolution,[],[f191,f5]) ).
fof(f1354,plain,
( ! [X0] :
( ~ sum(a,X0,additive_identity)
| less_or_equal(X0,additive_identity)
| ~ sum(a,X0,X0) )
| ~ spl0_4 ),
inference(factoring,[],[f525]) ).
fof(f1366,plain,
( ! [X0] :
( ~ sum(a,X0,X0)
| less_or_equal(X0,additive_identity)
| ~ sum(X0,a,additive_identity) )
| ~ spl0_4 ),
inference(resolution,[],[f1354,f5]) ).
fof(f1378,plain,
( ! [X0] :
( ~ sum(X0,a,additive_identity)
| less_or_equal(X0,additive_identity)
| ~ sum(X0,a,X0) )
| ~ spl0_4 ),
inference(resolution,[],[f1366,f5]) ).
fof(f1386,plain,
( less_or_equal(additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(a),a,additive_inverse(a))
| ~ defined(a)
| ~ spl0_4 ),
inference(resolution,[],[f1378,f4]) ).
fof(f1391,plain,
( ~ sum(additive_inverse(a),a,additive_inverse(a))
| ~ defined(a)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1386,f29]) ).
fof(f1392,plain,
( ~ sum(additive_inverse(a),a,additive_inverse(a))
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1391,f27]) ).
fof(f1400,plain,
( ! [X2,X0,X1] :
( ~ sum(X0,X2,additive_inverse(a))
| ~ sum(X1,a,X2)
| ~ sum(X0,X1,additive_inverse(a)) )
| ~ spl0_4 ),
inference(resolution,[],[f1392,f2]) ).
fof(f1436,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(a))
| ~ sum(X1,a,X1) )
| ~ spl0_4 ),
inference(factoring,[],[f1400]) ).
fof(f1453,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(a))
| ~ sum(X0,a,X0) )
| ~ spl0_4 ),
inference(resolution,[],[f1436,f5]) ).
fof(f1462,plain,
( ~ sum(additive_identity,a,additive_identity)
| ~ defined(additive_inverse(a))
| ~ spl0_4 ),
inference(resolution,[],[f1453,f3]) ).
fof(f1472,definition,
( spl0_37
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f1473,plain,
( ~ sum(additive_identity,a,additive_identity)
| spl0_37 ),
inference(avatar_component_clause,[],[f1472]) ).
fof(f1475,plain,
( ~ spl0_1
| ~ spl0_37
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f1462,f51,f1472,f39]) ).
fof(f1487,plain,
( ~ less_or_equal(a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| spl0_37 ),
inference(resolution,[],[f1473,f21]) ).
fof(f1491,plain,
( ~ less_or_equal(additive_identity,a)
| ~ spl0_4
| spl0_37 ),
inference(forward_subsumption_resolution,[],[f1487,f194]) ).
fof(f1492,plain,
( $false
| ~ spl0_4
| spl0_37 ),
inference(forward_subsumption_resolution,[],[f1491,f28]) ).
fof(f1493,plain,
( ~ spl0_4
| spl0_37 ),
inference(avatar_contradiction_clause,[],[f1492]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f56]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_37 ),
inference(sat_conversion,[],[f1475]) ).
cnf(s46,plain,
( ~ spl0_4
| spl0_37 ),
inference(sat_conversion,[],[f1493]) ).
cnf(s55,plain,
spl0_4,
inference(rat,[],[s3,s4]) ).
cnf(s56,plain,
spl0_37,
inference(rat,[],[s46,s55]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s45,s4,s56,s55]) ).
fof(f1494,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 00:51:02 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.22 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
% 2.93/1.18 % (3205598)Input is clausal, will run a generic CNF schedule.
% 2.93/1.18 % (3205607)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1611609804:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.93/1.18 % (3205607)First to succeed.
% 2.93/1.18 % (3205607)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3205598"
% 2.93/1.18 % (3205603)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=2298275820:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.93/1.18 % (3205606)lrs+10_1_sil=8000:sp=occurrence:random_seed=1239218294:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.93/1.18 % (3205604)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1423196821:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.93/1.18 % (3205608)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=750043224:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.93/1.18 % (3205609)dis-21_1_sil=8000:lcm=predicate:random_seed=914702014: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)
% 2.93/1.18 % (3205605)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2001384103:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.93/1.18 % (3205608)Also succeeded, but the first one will report.
% 2.93/1.18 % (3205609)Instruction limit reached!
% 2.93/1.18 % (3205609)------------------------------
% 2.93/1.18 % (3205609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.18 % (3205609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.18 % (3205609)CaDiCaL version: 2.1.3
% 2.93/1.18 % (3205609)Termination reason: Instruction limit
% 2.93/1.18 % (3205609)Termination phase: Saturation
% 2.93/1.18 % (3205609)Time elapsed: 0.058 s
% 2.93/1.18 % (3205609)Peak memory usage: 88 MB
% 2.93/1.18 % (3205609)Instructions burned: 118 (million)
% 2.93/1.18 % (3205606)Instruction limit reached!
% 2.93/1.18 % (3205606)------------------------------
% 2.93/1.18 % (3205606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.18 % (3205606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.18 % (3205606)CaDiCaL version: 2.1.3
% 2.93/1.18 % (3205606)Termination reason: Instruction limit
% 2.93/1.18 % (3205606)Termination phase: Saturation
% 2.93/1.18 % (3205606)Time elapsed: 0.061 s
% 2.93/1.18 % (3205606)Peak memory usage: 88 MB
% 2.93/1.18 % (3205606)Instructions burned: 108 (million)
% 2.93/1.18 % (3205607)Refutation found. Thanks to Tanya!
% 2.93/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.93/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.93/1.18 % (3205607)------------------------------
% 2.93/1.18 % (3205607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.19 % (3205607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.19 % (3205607)CaDiCaL version: 2.1.3
% 2.93/1.19 % (3205607)Termination reason: Refutation
% 2.93/1.19 % (3205607)Time elapsed: 0.027 s
% 2.93/1.19 % (3205607)Peak memory usage: 89 MB
% 2.93/1.19 % (3205607)Instructions burned: 85 (million)
% 2.93/1.19 % (3205607)------------------------------
% 2.93/1.19 % (3205607)------------------------------
% 2.93/1.19 % (3205598)Success in time 0.328 s
% 2.93/1.19 % Vampire exiting
%------------------------------------------------------------------------------