%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD058-3 : 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 : n009.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 09:49:16 AM UTC 2026
% Result : Unsatisfiable 2.92s 1.18s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 30 ( 12 unt; 2 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 26 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_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(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(f24,axiom,
! [X2,X3,X0,X1,X4] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X2,X3)
| ~ sum(X2,X4,X0)
| ~ sum(X3,X4,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(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f30,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f31,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
fof(f32,negated_conjecture,
sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
fof(f35,plain,
sum(additive_identity,a,a),
inference(resolution,[],[f3,f27]) ).
fof(f48,plain,
( ~ less_or_equal(a,additive_identity)
| ~ less_or_equal(additive_identity,a) ),
inference(resolution,[],[f21,f31]) ).
fof(f58,definition,
( spl0_3
<=> less_or_equal(additive_identity,a) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f59,plain,
( ~ less_or_equal(additive_identity,a)
| spl0_3 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_4
<=> less_or_equal(a,additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f62,plain,
( ~ less_or_equal(a,additive_identity)
| spl0_4 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f48,f61,f58]) ).
fof(f267,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f59,f29]) ).
fof(f270,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f1108,plain,
( ! [X2,X0,X1] :
( ~ less_or_equal(X0,X1)
| ~ sum(X0,X2,a)
| ~ sum(X1,X2,additive_identity) )
| spl0_4 ),
inference(resolution,[],[f24,f62]) ).
fof(f1138,plain,
( ! [X0] :
( ~ sum(b,X0,additive_identity)
| ~ sum(a,X0,a) )
| spl0_4 ),
inference(resolution,[],[f1108,f30]) ).
fof(f1170,plain,
( ! [X0] :
( ~ sum(a,X0,a)
| ~ sum(X0,b,additive_identity) )
| spl0_4 ),
inference(resolution,[],[f1138,f5]) ).
fof(f1330,plain,
( ! [X0] :
( ~ sum(X0,b,additive_identity)
| ~ sum(X0,a,a) )
| spl0_4 ),
inference(resolution,[],[f1170,f5]) ).
fof(f1969,plain,
( ~ sum(additive_identity,a,a)
| spl0_4 ),
inference(resolution,[],[f1330,f32]) ).
fof(f2111,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f1969,f35]) ).
fof(f2115,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f2111]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s23,plain,
spl0_3,
inference(sat_conversion,[],[f270]) ).
cnf(s215,plain,
spl0_4,
inference(sat_conversion,[],[f2115]) ).
cnf(s226,plain,
$false,
inference(rat,[],[s2,s215,s23]) ).
fof(f2116,plain,
$false,
inference(avatar_sat_refutation,[],[s226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD058-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 00:43:30 UTC 2026
% 0.07/0.17 % 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
% 0.07/0.21 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
% 2.92/1.18 % (3660705)Input is clausal, will run a generic CNF schedule.
% 2.92/1.18 % (3660716)dis-21_1_sil=8000:lcm=predicate:random_seed=2116970423: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)
% 2.92/1.18 % (3660716)First to succeed.
% 2.92/1.18 % (3660716)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3660705"
% 2.92/1.18 % (3660714)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2578466422:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.92/1.18 % (3660710)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=2237367561:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.92/1.18 % (3660715)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2215518869:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.92/1.18 % (3660711)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1606398377:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.92/1.18 % (3660713)lrs+10_1_sil=8000:sp=occurrence:random_seed=350130342:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.92/1.18 % (3660712)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=269412350:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.92/1.18 % (3660714)Also succeeded, but the first one will report.
% 2.92/1.18 % (3660713)Also succeeded, but the first one will report.
% 2.92/1.18 % (3660715)Also succeeded, but the first one will report.
% 2.92/1.18 % (3660716)Refutation found. Thanks to Tanya!
% 2.92/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.92/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.92/1.18 % (3660716)------------------------------
% 2.92/1.18 % (3660716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.18 % (3660716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.18 % (3660716)CaDiCaL version: 2.1.3
% 2.92/1.18 % (3660716)Termination reason: Refutation
% 2.92/1.18 % (3660716)Time elapsed: 0.017 s
% 2.92/1.18 % (3660716)Peak memory usage: 89 MB
% 2.92/1.18 % (3660716)Instructions burned: 52 (million)
% 2.92/1.18 % (3660716)------------------------------
% 2.92/1.18 % (3660716)------------------------------
% 2.92/1.18 % (3660705)Success in time 0.327 s
% 2.92/1.18 % Vampire exiting
%------------------------------------------------------------------------------