%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD067-3 : 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 : n016.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 09:49:19 AM UTC 2026
% Result : Unsatisfiable 3.69s 1.30s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 30 ( 10 unt; 2 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 73 ( 40 ~; 31 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f19,axiom,
! [X0,X1] :
( sum(X0,X1,add(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_addition) ).
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/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
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,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( less_or_equal(X3,add(X1,X2))
| ~ sum(X0,X2,X3)
| ~ less_or_equal(X0,X1)
| ~ defined(X1)
| ~ defined(X2) ),
inference(resolution,[],[f24,f19]) ).
fof(f243,plain,
! [X0] :
( ~ sum(X0,additive_inverse(a),additive_identity)
| ~ less_or_equal(X0,b)
| ~ defined(b)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[],[f74,f30]) ).
fof(f256,plain,
! [X0] :
( ~ sum(X0,additive_inverse(a),additive_identity)
| ~ less_or_equal(X0,b)
| ~ defined(additive_inverse(a)) ),
inference(forward_subsumption_resolution,[],[f243,f28]) ).
fof(f258,definition,
( spl0_17
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f259,plain,
( ~ defined(additive_inverse(a))
| spl0_17 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f285,definition,
( spl0_24
<=> ! [X0] :
( ~ sum(X0,additive_inverse(a),additive_identity)
| ~ less_or_equal(X0,b) ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f286,plain,
( ! [X0] :
( ~ sum(X0,additive_inverse(a),additive_identity)
| ~ less_or_equal(X0,b) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f287,plain,
( ~ spl0_17
| spl0_24 ),
inference(avatar_split_clause,[],[f256,f285,f258]) ).
fof(f288,plain,
( ~ defined(a)
| spl0_17 ),
inference(resolution,[],[f259,f15]) ).
fof(f289,plain,
( $false
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f288,f27]) ).
fof(f290,plain,
spl0_17,
inference(avatar_contradiction_clause,[],[f289]) ).
fof(f344,plain,
( ! [X0] :
( ~ sum(additive_inverse(a),X0,additive_identity)
| ~ less_or_equal(X0,b) )
| ~ spl0_24 ),
inference(resolution,[],[f286,f5]) ).
fof(f454,plain,
( ~ less_or_equal(a,b)
| ~ defined(a)
| ~ spl0_24 ),
inference(resolution,[],[f344,f4]) ).
fof(f458,plain,
( ~ defined(a)
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f454,f29]) ).
fof(f459,plain,
( $false
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f458,f27]) ).
fof(f460,plain,
~ spl0_24,
inference(avatar_contradiction_clause,[],[f459]) ).
cnf(s22,plain,
( ~ spl0_17
| spl0_24 ),
inference(sat_conversion,[],[f287]) ).
cnf(s23,plain,
spl0_17,
inference(sat_conversion,[],[f290]) ).
cnf(s34,plain,
~ spl0_24,
inference(sat_conversion,[],[f460]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s22,s34,s23]) ).
fof(f461,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD067-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 00:53:04 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.69/1.30 % (17321)Input is clausal, will run a generic CNF schedule.
% 3.69/1.30 % (17326)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=3955622953:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.69/1.30 % (17330)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2230745026:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.69/1.30 % (17329)lrs+10_1_sil=8000:sp=occurrence:random_seed=4183879416:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.69/1.30 % (17327)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4173058210:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.69/1.30 % (17332)dis-21_1_sil=8000:lcm=predicate:random_seed=1467216183: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)
% 3.69/1.30 % (17328)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2478748619:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.69/1.30 % (17331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1434378750:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.69/1.30 % (17331)Also succeeded, but the first one will report.
% 3.69/1.30 % (17330)First to succeed.
% 3.69/1.30 % (17330)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17321"
% 3.69/1.30 % (17329)Instruction limit reached!
% 3.69/1.30 % (17329)------------------------------
% 3.69/1.30 % (17329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.30 % (17329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.30 % (17329)CaDiCaL version: 2.1.3
% 3.69/1.30 % (17329)Termination reason: Instruction limit
% 3.69/1.30 % (17329)Termination phase: Saturation
% 3.69/1.30 % (17329)Time elapsed: 0.060 s
% 3.69/1.30 % (17329)Peak memory usage: 88 MB
% 3.69/1.30 % (17329)Instructions burned: 108 (million)
% 3.69/1.30 % (17332)Instruction limit reached!
% 3.69/1.30 % (17332)------------------------------
% 3.69/1.30 % (17332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.30 % (17332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.30 % (17332)CaDiCaL version: 2.1.3
% 3.69/1.30 % (17332)Termination reason: Instruction limit
% 3.69/1.30 % (17332)Termination phase: Saturation
% 3.69/1.30 % (17332)Time elapsed: 0.069 s
% 3.69/1.30 % (17332)Peak memory usage: 89 MB
% 3.69/1.30 % (17332)Instructions burned: 117 (million)
% 3.69/1.30 % (17340)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=3523722545:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.69/1.30 % (17341)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2020401727:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.69/1.30 % (17330)Refutation found. Thanks to Tanya!
% 3.69/1.30 % SZS status Unsatisfiable for theBenchmark
% 3.69/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.30 % (17330)------------------------------
% 3.69/1.30 % (17330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.30 % (17330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.30 % (17330)CaDiCaL version: 2.1.3
% 3.69/1.30 % (17330)Termination reason: Refutation
% 3.69/1.30 % (17330)Time elapsed: 0.012 s
% 3.69/1.30 % (17330)Peak memory usage: 89 MB
% 3.69/1.30 % (17330)Instructions burned: 17 (million)
% 3.69/1.30 % (17330)------------------------------
% 3.69/1.30 % (17330)------------------------------
% 3.69/1.30 % (17321)Success in time 0.439 s
% 3.69/1.30 % Vampire exiting
%------------------------------------------------------------------------------