%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD067-2 : 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 : n019.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 4.11s 1.34s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 41 ( 13 unt; 2 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 40 ~; 40 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
fof(f18,axiom,
! [X0,X1] :
( less_or_equal(X0,X1)
| less_or_equal(X1,X0)
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f22,axiom,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1)
| ~ equalish(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f30,axiom,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
fof(f31,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f32,negated_conjecture,
equalish(add(b,additive_inverse(a)),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_u_5) ).
fof(f33,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_6) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( ~ less_or_equal(X1,X2)
| ~ defined(X0)
| less_or_equal(X3,add(X2,X0))
| ~ equalish(add(X1,X0),X3) ),
inference(resolution,[],[f19,f26]) ).
fof(f207,plain,
! [X0,X1] :
( ~ equalish(add(a,X0),X1)
| less_or_equal(X1,add(b,X0))
| ~ defined(X0) ),
inference(resolution,[],[f102,f31]) ).
fof(f261,plain,
( less_or_equal(additive_identity,add(b,additive_inverse(a)))
| ~ defined(additive_inverse(a))
| ~ defined(a) ),
inference(resolution,[],[f207,f3]) ).
fof(f268,plain,
( less_or_equal(additive_identity,add(b,additive_inverse(a)))
| ~ defined(a) ),
inference(forward_subsumption_resolution,[],[f261,f12]) ).
fof(f271,plain,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(forward_subsumption_resolution,[],[f268,f28]) ).
fof(f280,plain,
! [X0] :
( ~ less_or_equal(add(b,additive_inverse(a)),X0)
| less_or_equal(additive_identity,X0) ),
inference(resolution,[],[f271,f17]) ).
fof(f377,definition,
( spl0_19
<=> less_or_equal(add(b,additive_inverse(a)),u) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f378,plain,
( less_or_equal(add(b,additive_inverse(a)),u)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f443,definition,
( spl0_26
<=> less_or_equal(u,u) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f444,plain,
( less_or_equal(u,u)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
( ~ less_or_equal(u,u)
| spl0_26 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f456,plain,
( less_or_equal(u,u)
| ~ defined(u)
| ~ defined(u)
| spl0_26 ),
inference(resolution,[],[f445,f18]) ).
fof(f457,plain,
( less_or_equal(u,u)
| ~ defined(u)
| spl0_26 ),
inference(duplicate_literal_removal,[],[f456]) ).
fof(f458,plain,
( ~ defined(u)
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f457,f445]) ).
fof(f459,plain,
( $false
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f458,f30]) ).
fof(f460,plain,
spl0_26,
inference(avatar_contradiction_clause,[],[f459]) ).
fof(f470,plain,
( ! [X0] :
( ~ equalish(u,X0)
| less_or_equal(X0,u) )
| ~ spl0_26 ),
inference(resolution,[],[f444,f26]) ).
fof(f628,plain,
( ! [X0] :
( ~ equalish(X0,u)
| less_or_equal(X0,u) )
| ~ spl0_26 ),
inference(resolution,[],[f470,f22]) ).
fof(f769,plain,
( less_or_equal(add(b,additive_inverse(a)),u)
| ~ spl0_26 ),
inference(resolution,[],[f628,f32]) ).
fof(f777,plain,
( spl0_19
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f769,f443,f377]) ).
fof(f4186,plain,
( less_or_equal(additive_identity,u)
| ~ spl0_19 ),
inference(resolution,[],[f280,f378]) ).
fof(f4192,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f4186,f33]) ).
fof(f4193,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[],[f4192]) ).
cnf(s21,plain,
spl0_26,
inference(sat_conversion,[],[f460]) ).
cnf(s27,plain,
( spl0_19
| ~ spl0_26 ),
inference(sat_conversion,[],[f777]) ).
cnf(s208,plain,
~ spl0_19,
inference(sat_conversion,[],[f4193]) ).
cnf(s226,plain,
~ spl0_26,
inference(rat,[],[s27,s208]) ).
cnf(s231,plain,
$false,
inference(rat,[],[s21,s226]) ).
fof(f4229,plain,
$false,
inference(avatar_sat_refutation,[],[s231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD067-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 00:48:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 4.11/1.34 % (429547)Input is clausal, will run a generic CNF schedule.
% 4.11/1.34 % (429555)lrs+10_1_sil=8000:sp=occurrence:random_seed=643009701:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.11/1.34 % (429557)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=679227745:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.11/1.34 % (429558)dis-21_1_sil=8000:lcm=predicate:random_seed=3220228653: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)
% 4.11/1.34 % (429553)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3483232745:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.11/1.34 % (429552)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=2787631196:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.11/1.34 % (429554)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=674500315:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.11/1.34 % (429556)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1616284011:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.11/1.34 % (429555)Instruction limit reached!
% 4.11/1.34 % (429555)------------------------------
% 4.11/1.34 % (429555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.34 % (429555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.34 % (429555)CaDiCaL version: 2.1.3
% 4.11/1.34 % (429555)Termination reason: Instruction limit
% 4.11/1.34 % (429555)Termination phase: Saturation
% 4.11/1.34 % (429555)Time elapsed: 0.038 s
% 4.11/1.34 % (429555)Peak memory usage: 89 MB
% 4.11/1.34 % (429555)Instructions burned: 107 (million)
% 4.11/1.34 % (429558)Instruction limit reached!
% 4.11/1.34 % (429558)------------------------------
% 4.11/1.34 % (429558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.34 % (429558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.34 % (429558)CaDiCaL version: 2.1.3
% 4.11/1.34 % (429558)Termination reason: Instruction limit
% 4.11/1.34 % (429558)Termination phase: Saturation
% 4.11/1.34 % (429558)Time elapsed: 0.064 s
% 4.11/1.34 % (429558)Peak memory usage: 89 MB
% 4.11/1.34 % (429558)Instructions burned: 117 (million)
% 4.11/1.34 % (429556)Instruction limit reached!
% 4.11/1.34 % (429556)------------------------------
% 4.11/1.34 % (429556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.34 % (429556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.34 % (429556)CaDiCaL version: 2.1.3
% 4.11/1.34 % (429556)Termination reason: Instruction limit
% 4.11/1.34 % (429556)Termination phase: Saturation
% 4.11/1.34 % (429556)Time elapsed: 0.067 s
% 4.11/1.34 % (429556)Peak memory usage: 88 MB
% 4.11/1.34 % (429556)Instructions burned: 115 (million)
% 4.11/1.34 % (429557)First to succeed.
% 4.11/1.34 % (429557)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-429547"
% 4.11/1.34 % (429566)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=1662158518:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.11/1.34 % (429566)Instruction limit reached!
% 4.11/1.34 % (429566)------------------------------
% 4.11/1.34 % (429566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.34 % (429566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.34 % (429566)CaDiCaL version: 2.1.3
% 4.11/1.34 % (429566)Termination reason: Instruction limit
% 4.11/1.34 % (429566)Termination phase: Saturation
% 4.11/1.34 % (429566)Time elapsed: 0.047 s
% 4.11/1.34 % (429566)Peak memory usage: 89 MB
% 4.11/1.34 % (429566)Instructions burned: 146 (million)
% 4.11/1.34 % (429567)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2418589447: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)
% 4.11/1.34 % (429568)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2507248401:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.11/1.34 % (429570)lrs+10_64_to=lpo:sil=8000:random_seed=3530241930:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.11/1.34 % (429567)Instruction limit reached!
% 4.11/1.34 % (429567)------------------------------
% 4.11/1.34 % (429567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.34 % (429567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.34 % (429567)CaDiCaL version: 2.1.3
% 4.11/1.34 % (429567)Termination reason: Instruction limit
% 4.11/1.34 % (429567)Termination phase: Saturation
% 4.11/1.34 % (429567)Time elapsed: 0.095 s
% 4.11/1.34 % (429567)Peak memory usage: 94 MB
% 4.11/1.34 % (429567)Instructions burned: 190 (million)
% 4.11/1.34 % (429570)Instruction limit reached!
% 4.11/1.34 % (429570)------------------------------
% 4.11/1.34 % (429570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.34 % (429570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.34 % (429570)CaDiCaL version: 2.1.3
% 4.11/1.34 % (429570)Termination reason: Instruction limit
% 4.11/1.34 % (429570)Termination phase: Saturation
% 4.11/1.34 % (429570)Time elapsed: 0.044 s
% 4.11/1.34 % (429570)Peak memory usage: 89 MB
% 4.11/1.34 % (429570)Instructions burned: 128 (million)
% 4.11/1.34 % (429568)Instruction limit reached!
% 4.11/1.34 % (429568)------------------------------
% 4.11/1.34 % (429568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.34 % (429568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.34 % (429568)CaDiCaL version: 2.1.3
% 4.11/1.34 % (429568)Termination reason: Instruction limit
% 4.11/1.34 % (429568)Termination phase: Saturation
% 4.11/1.34 % (429568)Time elapsed: 0.126 s
% 4.11/1.34 % (429568)Peak memory usage: 88 MB
% 4.11/1.34 % (429568)Instructions burned: 220 (million)
% 4.11/1.34 % (429557)Refutation found. Thanks to Tanya!
% 4.11/1.34 % SZS status Unsatisfiable for theBenchmark
% 4.11/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 4.11/1.34 % (429557)------------------------------
% 4.11/1.34 % (429557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.34 % (429557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.34 % (429557)CaDiCaL version: 2.1.3
% 4.11/1.34 % (429557)Termination reason: Refutation
% 4.11/1.34 % (429557)Time elapsed: 0.096 s
% 4.11/1.34 % (429557)Peak memory usage: 90 MB
% 4.11/1.34 % (429557)Instructions burned: 138 (million)
% 4.11/1.34 % (429557)------------------------------
% 4.11/1.34 % (429557)------------------------------
% 4.11/1.34 % (429547)Success in time 0.492 s
% 4.11/1.34 % Vampire exiting
%------------------------------------------------------------------------------