%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD014-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 09:49:01 AM UTC 2026
% Result : Unsatisfiable 3.57s 1.27s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 13 unt; 3 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 74 ~; 55 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
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/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
fof(f31,plain,
~ sum(additive_inverse(a),additive_identity,additive_inverse(b)),
inference(resolution,[],[f5,f30]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ sum(additive_inverse(a),X0,X1)
| ~ sum(X0,X2,additive_identity)
| ~ sum(X1,X2,additive_inverse(b)) ),
inference(resolution,[],[f31,f1]) ).
fof(f42,definition,
( spl0_1
<=> defined(additive_inverse(b)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f43,plain,
( ~ defined(additive_inverse(b))
| spl0_1 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f65,plain,
( ~ defined(b)
| spl0_1 ),
inference(resolution,[],[f43,f15]) ).
fof(f66,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f65,f28]) ).
fof(f67,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f66]) ).
fof(f93,plain,
! [X0] :
( ~ sum(a,X0,additive_identity)
| ~ sum(additive_identity,X0,additive_inverse(b))
| ~ defined(a) ),
inference(resolution,[],[f33,f4]) ).
fof(f98,plain,
! [X0] :
( ~ sum(additive_identity,X0,additive_inverse(b))
| ~ sum(a,X0,additive_identity) ),
inference(forward_subsumption_resolution,[],[f93,f27]) ).
fof(f194,plain,
( ~ sum(a,additive_inverse(b),additive_identity)
| ~ defined(additive_inverse(b)) ),
inference(resolution,[],[f98,f3]) ).
fof(f199,definition,
( spl0_18
<=> sum(a,additive_inverse(b),additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f200,plain,
( ~ sum(a,additive_inverse(b),additive_identity)
| spl0_18 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f201,plain,
( ~ spl0_1
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f194,f199,f42]) ).
fof(f212,plain,
( ! [X2,X0,X1] :
( ~ sum(X1,additive_inverse(b),X2)
| ~ sum(X0,X1,a)
| ~ sum(X0,X2,additive_identity) )
| spl0_18 ),
inference(resolution,[],[f200,f2]) ).
fof(f474,plain,
( ! [X0] :
( ~ sum(X0,additive_identity,a)
| ~ sum(X0,additive_inverse(b),additive_identity)
| ~ defined(additive_inverse(b)) )
| spl0_18 ),
inference(resolution,[],[f212,f3]) ).
fof(f485,definition,
( spl0_48
<=> ! [X0] :
( ~ sum(X0,additive_identity,a)
| ~ sum(X0,additive_inverse(b),additive_identity) ) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f486,plain,
( ! [X0] :
( ~ sum(X0,additive_inverse(b),additive_identity)
| ~ sum(X0,additive_identity,a) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f487,plain,
( ~ spl0_1
| spl0_48
| spl0_18 ),
inference(avatar_split_clause,[],[f474,f199,f485,f42]) ).
fof(f497,plain,
( ! [X0] :
( ~ sum(additive_inverse(b),X0,additive_identity)
| ~ sum(X0,additive_identity,a) )
| ~ spl0_48 ),
inference(resolution,[],[f486,f5]) ).
fof(f543,plain,
( ~ sum(b,additive_identity,a)
| ~ defined(b)
| ~ spl0_48 ),
inference(resolution,[],[f497,f4]) ).
fof(f547,plain,
( ~ sum(b,additive_identity,a)
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[],[f543,f28]) ).
fof(f552,plain,
( ! [X2,X0,X1] :
( ~ sum(X1,additive_identity,X2)
| ~ sum(X0,X1,b)
| ~ sum(X0,X2,a) )
| ~ spl0_48 ),
inference(resolution,[],[f547,f2]) ).
fof(f586,plain,
( ! [X0] :
( ~ sum(X0,additive_identity,b)
| ~ sum(X0,additive_identity,a)
| ~ defined(additive_identity) )
| ~ spl0_48 ),
inference(resolution,[],[f552,f3]) ).
fof(f593,plain,
( ! [X0] :
( ~ sum(X0,additive_identity,b)
| ~ sum(X0,additive_identity,a) )
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[],[f586,f14]) ).
fof(f605,plain,
( ! [X0] :
( ~ sum(additive_identity,X0,b)
| ~ sum(X0,additive_identity,a) )
| ~ spl0_48 ),
inference(resolution,[],[f593,f5]) ).
fof(f617,plain,
( ~ sum(a,additive_identity,a)
| ~ spl0_48 ),
inference(resolution,[],[f605,f29]) ).
fof(f635,plain,
( ~ sum(additive_identity,a,a)
| ~ spl0_48 ),
inference(resolution,[],[f617,f5]) ).
fof(f647,plain,
( ~ defined(a)
| ~ spl0_48 ),
inference(resolution,[],[f635,f3]) ).
fof(f651,plain,
( $false
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[],[f647,f27]) ).
fof(f652,plain,
~ spl0_48,
inference(avatar_contradiction_clause,[],[f651]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f67]) ).
cnf(s16,plain,
( ~ spl0_1
| ~ spl0_18 ),
inference(sat_conversion,[],[f201]) ).
cnf(s43,plain,
( ~ spl0_1
| spl0_18
| spl0_48 ),
inference(sat_conversion,[],[f487]) ).
cnf(s52,plain,
~ spl0_48,
inference(sat_conversion,[],[f652]) ).
cnf(s53,plain,
( ~ spl0_1
| spl0_18 ),
inference(rat,[],[s43,s52]) ).
cnf(s69,plain,
spl0_18,
inference(rat,[],[s53,s4]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s16,s69,s4]) ).
fof(f653,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD014-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 00:26:48 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 3.57/1.27 % (2513374)Input is clausal, will run a generic CNF schedule.
% 3.57/1.27 % (2513379)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=1501088474:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.57/1.27 % (2513381)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2983568041:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.57/1.27 % (2513384)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3608864984:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.57/1.27 % (2513380)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2770615530:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.57/1.27 % (2513385)dis-21_1_sil=8000:lcm=predicate:random_seed=3643047598: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)
% 3.57/1.27 % (2513382)lrs+10_1_sil=8000:sp=occurrence:random_seed=3272665177:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.57/1.27 % (2513383)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3646364484:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.57/1.27 % (2513383)First to succeed.
% 3.57/1.27 % (2513383)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2513374"
% 3.57/1.27 % (2513382)Also succeeded, but the first one will report.
% 3.57/1.27 % (2513384)Also succeeded, but the first one will report.
% 3.57/1.27 % (2513385)Instruction limit reached!
% 3.57/1.27 % (2513385)------------------------------
% 3.57/1.27 % (2513385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.27 % (2513385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.27 % (2513385)CaDiCaL version: 2.1.3
% 3.57/1.27 % (2513385)Termination reason: Instruction limit
% 3.57/1.27 % (2513385)Termination phase: Saturation
% 3.57/1.27 % (2513385)Time elapsed: 0.077 s
% 3.57/1.27 % (2513385)Peak memory usage: 89 MB
% 3.57/1.27 % (2513385)Instructions burned: 118 (million)
% 3.57/1.27 % (2513393)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=3669099734:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.57/1.27 % (2513383)Refutation found. Thanks to Tanya!
% 3.57/1.27 % SZS status Unsatisfiable for theBenchmark
% 3.57/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.27 % (2513383)------------------------------
% 3.57/1.27 % (2513383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.27 % (2513383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.27 % (2513383)CaDiCaL version: 2.1.3
% 3.57/1.27 % (2513383)Termination reason: Refutation
% 3.57/1.27 % (2513383)Time elapsed: 0.016 s
% 3.57/1.27 % (2513383)Peak memory usage: 89 MB
% 3.57/1.27 % (2513383)Instructions burned: 23 (million)
% 3.57/1.27 % (2513383)------------------------------
% 3.57/1.27 % (2513383)------------------------------
% 3.57/1.27 % (2513374)Success in time 0.422 s
% 3.57/1.27 % Vampire exiting
%------------------------------------------------------------------------------