%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD059-2 : 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 : 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 3.27s 1.17s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 69 ( 19 unt; 5 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 151 ( 72 ~; 74 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f16,axiom,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
fof(f18,axiom,
! [X0,X1] :
( less_or_equal(X1,X0)
| less_or_equal(X0,X1)
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_order_relation) ).
fof(f19,axiom,
! [X2,X0,X1] :
( less_or_equal(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ less_or_equal(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f22,axiom,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1)
| ~ equalish(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
fof(f30,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f31,negated_conjecture,
equalish(add(a,a),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_equals_u_4) ).
fof(f32,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_5) ).
fof(f33,plain,
equalish(u,add(a,a)),
inference(resolution,[],[f22,f31]) ).
fof(f50,plain,
! [X0] :
( ~ less_or_equal(X0,additive_identity)
| less_or_equal(X0,a) ),
inference(resolution,[],[f17,f30]) ).
fof(f54,plain,
! [X0] :
( ~ equalish(X0,add(a,a))
| equalish(X0,u) ),
inference(resolution,[],[f23,f31]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ equalish(X0,X2)
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X0) ),
inference(resolution,[],[f18,f26]) ).
fof(f74,plain,
! [X0] :
( less_or_equal(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[],[f18]) ).
fof(f75,plain,
! [X0] :
( less_or_equal(X0,X0)
| ~ defined(X0) ),
inference(duplicate_literal_removal,[],[f74]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ equalish(add(X1,X0),X3)
| ~ less_or_equal(X1,X2)
| less_or_equal(X3,add(X2,X0))
| ~ defined(X0) ),
inference(resolution,[],[f19,f26]) ).
fof(f158,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| less_or_equal(X1,X0)
| ~ defined(X0) ),
inference(resolution,[],[f75,f26]) ).
fof(f180,definition,
( spl0_10
<=> less_or_equal(add(a,a),a) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f182,plain,
( less_or_equal(add(a,a),a)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f258,plain,
! [X0] :
( ~ defined(u)
| ~ defined(X0)
| less_or_equal(add(a,a),X0)
| less_or_equal(X0,u) ),
inference(resolution,[],[f69,f33]) ).
fof(f267,plain,
! [X0] :
( less_or_equal(add(a,a),X0)
| ~ defined(X0)
| less_or_equal(X0,u) ),
inference(forward_subsumption_resolution,[],[f258,f29]) ).
fof(f420,plain,
! [X0,X1] :
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(X1,add(X0,X1))
| ~ defined(X1)
| ~ defined(X1) ),
inference(resolution,[],[f131,f2]) ).
fof(f437,plain,
! [X0,X1] :
( less_or_equal(X1,add(X0,X1))
| ~ less_or_equal(additive_identity,X0)
| ~ defined(X1) ),
inference(duplicate_literal_removal,[],[f420]) ).
fof(f680,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_identity,u)
| less_or_equal(add(a,a),a) ),
inference(resolution,[],[f267,f50]) ).
fof(f683,plain,
( less_or_equal(additive_identity,u)
| less_or_equal(add(a,a),a) ),
inference(forward_subsumption_resolution,[],[f680,f11]) ).
fof(f685,plain,
less_or_equal(add(a,a),a),
inference(forward_subsumption_resolution,[],[f683,f32]) ).
fof(f686,plain,
spl0_10,
inference(avatar_split_clause,[],[f685,f180]) ).
fof(f690,plain,
( ~ less_or_equal(a,add(a,a))
| equalish(a,add(a,a))
| ~ spl0_10 ),
inference(resolution,[],[f182,f16]) ).
fof(f692,definition,
( spl0_34
<=> equalish(a,add(a,a)) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f694,plain,
( equalish(a,add(a,a))
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f696,definition,
( spl0_35
<=> less_or_equal(a,add(a,a)) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f698,plain,
( ~ less_or_equal(a,add(a,a))
| spl0_35 ),
inference(avatar_component_clause,[],[f696]) ).
fof(f699,plain,
( spl0_34
| ~ spl0_35
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f690,f180,f696,f692]) ).
fof(f726,definition,
( spl0_37
<=> equalish(a,u) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f728,plain,
( equalish(a,u)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f730,definition,
( spl0_38
<=> less_or_equal(a,u) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f731,plain,
( less_or_equal(a,u)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f732,plain,
( ~ less_or_equal(a,u)
| spl0_38 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f1107,plain,
( ~ less_or_equal(additive_identity,a)
| ~ defined(a)
| spl0_35 ),
inference(resolution,[],[f437,f698]) ).
fof(f1109,plain,
( ~ defined(a)
| spl0_35 ),
inference(forward_subsumption_resolution,[],[f1107,f30]) ).
fof(f1110,plain,
( $false
| spl0_35 ),
inference(forward_subsumption_resolution,[],[f1109,f28]) ).
fof(f1111,plain,
spl0_35,
inference(avatar_contradiction_clause,[],[f1110]) ).
fof(f1112,plain,
( equalish(a,u)
| ~ spl0_34 ),
inference(resolution,[],[f694,f54]) ).
fof(f1121,plain,
( spl0_37
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1112,f692,f726]) ).
fof(f1147,plain,
( equalish(u,a)
| ~ spl0_37 ),
inference(resolution,[],[f728,f22]) ).
fof(f1170,plain,
( less_or_equal(a,u)
| ~ defined(u)
| ~ spl0_37 ),
inference(resolution,[],[f1147,f158]) ).
fof(f1175,plain,
( ~ defined(u)
| ~ spl0_37
| spl0_38 ),
inference(forward_subsumption_resolution,[],[f1170,f732]) ).
fof(f1176,plain,
( $false
| ~ spl0_37
| spl0_38 ),
inference(forward_subsumption_resolution,[],[f1175,f29]) ).
fof(f1177,plain,
( ~ spl0_37
| spl0_38 ),
inference(avatar_contradiction_clause,[],[f1176]) ).
fof(f1197,plain,
( ! [X0] :
( ~ less_or_equal(X0,a)
| less_or_equal(X0,u) )
| ~ spl0_38 ),
inference(resolution,[],[f731,f17]) ).
fof(f2136,plain,
( less_or_equal(additive_identity,u)
| ~ spl0_38 ),
inference(resolution,[],[f1197,f30]) ).
fof(f2143,plain,
( $false
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f2136,f32]) ).
fof(f2144,plain,
~ spl0_38,
inference(avatar_contradiction_clause,[],[f2143]) ).
cnf(s24,plain,
spl0_10,
inference(sat_conversion,[],[f686]) ).
cnf(s25,plain,
( ~ spl0_10
| spl0_34
| ~ spl0_35 ),
inference(sat_conversion,[],[f699]) ).
cnf(s35,plain,
spl0_35,
inference(sat_conversion,[],[f1111]) ).
cnf(s36,plain,
( ~ spl0_34
| spl0_37 ),
inference(sat_conversion,[],[f1121]) ).
cnf(s37,plain,
( ~ spl0_37
| spl0_38 ),
inference(sat_conversion,[],[f1177]) ).
cnf(s50,plain,
~ spl0_38,
inference(sat_conversion,[],[f2144]) ).
cnf(s57,plain,
~ spl0_37,
inference(rat,[],[s37,s50]) ).
cnf(s58,plain,
~ spl0_34,
inference(rat,[],[s36,s57]) ).
cnf(s62,plain,
~ spl0_10,
inference(rat,[],[s25,s35,s58]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s24,s62]) ).
fof(f2149,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n009.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 00:44:00 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running first-order theorem proving
% 0.09/0.25 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
% 3.27/1.17 % (3661979)Input is clausal, will run a generic CNF schedule.
% 3.27/1.17 % (3661999)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1585059633:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.27/1.17 % (3662000)lrs+10_1_sil=8000:sp=occurrence:random_seed=3469084791:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.27/1.17 % (3661996)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=3075567675:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.27/1.17 % (3661997)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2376501960:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.27/1.17 % (3662003)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3130500426:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.27/1.17 % (3662005)dis-21_1_sil=8000:lcm=predicate:random_seed=2367834593: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)
% 3.27/1.17 % (3662002)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=225586481:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.27/1.17 % (3662000)First to succeed.
% 3.27/1.17 % (3662000)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3661979"
% 3.27/1.17 % (3662005)Instruction limit reached!
% 3.27/1.17 % (3662005)------------------------------
% 3.27/1.17 % (3662005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.27/1.17 % (3662005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.27/1.17 % (3662005)CaDiCaL version: 2.1.3
% 3.27/1.17 % (3662005)Termination reason: Instruction limit
% 3.27/1.17 % (3662005)Termination phase: Saturation
% 3.27/1.17 % (3662005)Time elapsed: 0.051 s
% 3.27/1.17 % (3662005)Peak memory usage: 88 MB
% 3.27/1.17 % (3662005)Instructions burned: 118 (million)
% 3.27/1.17 % (3662002)Instruction limit reached!
% 3.27/1.17 % (3662002)------------------------------
% 3.27/1.17 % (3662002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.27/1.17 % (3662002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.27/1.17 % (3662002)CaDiCaL version: 2.1.3
% 3.27/1.17 % (3662002)Termination reason: Instruction limit
% 3.27/1.17 % (3662002)Termination phase: Saturation
% 3.27/1.17 % (3662002)Time elapsed: 0.069 s
% 3.27/1.17 % (3662002)Peak memory usage: 88 MB
% 3.27/1.17 % (3662002)Instructions burned: 115 (million)
% 3.27/1.17 % (3662003)Instruction limit reached!
% 3.27/1.17 % (3662003)------------------------------
% 3.27/1.17 % (3662003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.27/1.17 % (3662003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.27/1.17 % (3662003)CaDiCaL version: 2.1.3
% 3.27/1.17 % (3662003)Termination reason: Instruction limit
% 3.27/1.17 % (3662003)Termination phase: Saturation
% 3.27/1.17 % (3662003)Time elapsed: 0.127 s
% 3.27/1.17 % (3662003)Peak memory usage: 89 MB
% 3.27/1.17 % (3662003)Instructions burned: 180 (million)
% 3.27/1.17 % (3662091)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=3838533592:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.27/1.17 % (3662099)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1237009463: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)
% 3.27/1.17 % (3662114)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2969672076:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.27/1.17 % (3662000)Refutation found. Thanks to Tanya!
% 3.27/1.17 % SZS status Unsatisfiable for theBenchmark
% 3.27/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 3.82/1.36 % (3662000)------------------------------
% 3.82/1.36 % (3662000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.36 % (3662000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.36 % (3662000)CaDiCaL version: 2.1.3
% 3.82/1.36 % (3662000)Termination reason: Refutation
% 3.82/1.36 % (3662000)Time elapsed: 0.050 s
% 3.82/1.36 % (3662000)Peak memory usage: 90 MB
% 3.82/1.36 % (3662000)Instructions burned: 70 (million)
% 3.82/1.36 % (3662000)------------------------------
% 3.82/1.36 % (3662000)------------------------------
% 3.82/1.36 % (3661979)Success in time 0.433 s
% 3.82/1.36 % Vampire exiting
%------------------------------------------------------------------------------