%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD003-1 : 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 : n017.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 09:48:57 AM UTC 2026
% Result : Unsatisfiable 2.77s 1.25s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 9 unt; 2 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 74 ( 38 ~; 34 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 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(f3,axiom,
! [X0] :
( equalish(add(X0,additive_inverse(X0)),additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f4,axiom,
! [X0,X1] :
( equalish(add(X0,X1),add(X1,X0))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f10,axiom,
! [X0,X1] :
( defined(add(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_addition) ).
fof(f12,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f24,axiom,
! [X2,X0,X1] :
( equalish(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ equalish(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,negated_conjecture,
~ equalish(add(a,add(b,additive_inverse(b))),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_not_equal_to_a_3) ).
fof(f38,plain,
! [X0] :
( ~ equalish(add(a,add(b,additive_inverse(b))),X0)
| ~ equalish(X0,a) ),
inference(resolution,[],[f23,f30]) ).
fof(f61,plain,
( ~ defined(a)
| ~ defined(add(b,additive_inverse(b)))
| ~ equalish(add(add(b,additive_inverse(b)),a),a) ),
inference(resolution,[],[f4,f38]) ).
fof(f63,plain,
( ~ defined(add(b,additive_inverse(b)))
| ~ equalish(add(add(b,additive_inverse(b)),a),a) ),
inference(forward_subsumption_resolution,[],[f61,f28]) ).
fof(f65,definition,
( spl0_4
<=> equalish(add(add(b,additive_inverse(b)),a),a) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f67,plain,
( ~ equalish(add(add(b,additive_inverse(b)),a),a)
| spl0_4 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f69,definition,
( spl0_5
<=> defined(add(b,additive_inverse(b))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f71,plain,
( ~ defined(add(b,additive_inverse(b)))
| spl0_5 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f63,f69,f65]) ).
fof(f75,plain,
( ~ defined(b)
| ~ defined(additive_inverse(b))
| spl0_5 ),
inference(resolution,[],[f71,f10]) ).
fof(f76,plain,
( ~ defined(additive_inverse(b))
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f75,f29]) ).
fof(f78,plain,
( ~ defined(b)
| spl0_5 ),
inference(resolution,[],[f76,f12]) ).
fof(f79,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f78,f29]) ).
fof(f80,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f79]) ).
fof(f85,plain,
( ! [X0] :
( ~ equalish(X0,a)
| ~ equalish(add(add(b,additive_inverse(b)),a),X0) )
| spl0_4 ),
inference(resolution,[],[f67,f23]) ).
fof(f114,plain,
( ~ equalish(add(add(b,additive_inverse(b)),a),add(additive_identity,a))
| ~ defined(a)
| spl0_4 ),
inference(resolution,[],[f85,f2]) ).
fof(f118,plain,
( ~ equalish(add(add(b,additive_inverse(b)),a),add(additive_identity,a))
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f114,f28]) ).
fof(f133,plain,
( ~ defined(a)
| ~ equalish(add(b,additive_inverse(b)),additive_identity)
| spl0_4 ),
inference(resolution,[],[f118,f24]) ).
fof(f136,plain,
( ~ equalish(add(b,additive_inverse(b)),additive_identity)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f133,f28]) ).
fof(f143,plain,
( ~ defined(b)
| spl0_4 ),
inference(resolution,[],[f136,f3]) ).
fof(f146,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f143,f29]) ).
fof(f147,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f146]) ).
cnf(s3,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f72]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f80]) ).
cnf(s7,plain,
spl0_4,
inference(sat_conversion,[],[f147]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s5,s7]) ).
fof(f148,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD003-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:17:36 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.77/1.25 % (5827)Input is clausal, will run a generic CNF schedule.
% 2.77/1.25 % (5906)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4029380044:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.25 % (5906)First to succeed.
% 2.77/1.25 % (5906)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5827"
% 2.77/1.25 % (5898)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=77480144:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.25 % (5903)lrs+10_1_sil=8000:sp=occurrence:random_seed=2401253326:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.25 % (5900)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4125425153:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.25 % (5901)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2795680366:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.25 % (5904)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3787345227:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.25 % (5907)dis-21_1_sil=8000:lcm=predicate:random_seed=3582869746: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)
% 2.77/1.25 % (5904)Also succeeded, but the first one will report.
% 2.77/1.25 % (5903)Instruction limit reached!
% 2.77/1.25 % (5903)------------------------------
% 2.77/1.25 % (5903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.25 % (5903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.25 % (5903)CaDiCaL version: 2.1.3
% 2.77/1.25 % (5903)Termination reason: Instruction limit
% 2.77/1.25 % (5903)Termination phase: Saturation
% 2.77/1.25 % (5903)Time elapsed: 0.070 s
% 2.77/1.25 % (5903)Peak memory usage: 89 MB
% 2.77/1.25 % (5903)Instructions burned: 109 (million)
% 2.77/1.25 % (5907)Instruction limit reached!
% 2.77/1.25 % (5907)------------------------------
% 2.77/1.25 % (5907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.25 % (5907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.25 % (5907)CaDiCaL version: 2.1.3
% 2.77/1.25 % (5907)Termination reason: Instruction limit
% 2.77/1.25 % (5907)Termination phase: Saturation
% 2.77/1.25 % (5907)Time elapsed: 0.086 s
% 2.77/1.25 % (5907)Peak memory usage: 89 MB
% 2.77/1.25 % (5907)Instructions burned: 117 (million)
% 2.77/1.25 % (5906)Refutation found. Thanks to Tanya!
% 2.77/1.25 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.25 % (5906)------------------------------
% 2.77/1.25 % (5906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.25 % (5906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.25 % (5906)CaDiCaL version: 2.1.3
% 2.77/1.25 % (5906)Termination reason: Refutation
% 2.77/1.25 % (5906)Time elapsed: 0.003 s
% 2.77/1.25 % (5906)Peak memory usage: 89 MB
% 2.77/1.25 % (5906)Instructions burned: 4 (million)
% 2.77/1.25 % (5906)------------------------------
% 2.77/1.25 % (5906)------------------------------
% 2.77/1.25 % (5827)Success in time 0.298 s
% 2.77/1.25 % Vampire exiting
%------------------------------------------------------------------------------