%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD064-1 : 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 : n002.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 09:49:18 AM UTC 2026
% Result : Unsatisfiable 5.53s 1.57s
% Output : Refutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 38 ( 10 unt; 1 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 59 ~; 46 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 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(f3,axiom,
! [X0] :
( equalish(add(X0,additive_inverse(X0)),additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f12,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f17,axiom,
! [X2,X0,X1] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X0,X2)
| ~ less_or_equal(X2,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(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f26,axiom,
! [X2,X0,X1] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X2,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,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_2) ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_3) ).
fof(f42,plain,
! [X0] :
( ~ equalish(X0,additive_inverse(a))
| ~ less_or_equal(X0,additive_identity) ),
inference(resolution,[],[f30,f26]) ).
fof(f46,definition,
( spl0_3
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f47,plain,
( defined(additive_inverse(a))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( ~ defined(additive_inverse(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f57,plain,
( ~ defined(a)
| spl0_3 ),
inference(resolution,[],[f48,f12]) ).
fof(f58,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f57,f28]) ).
fof(f59,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f58]) ).
fof(f70,plain,
( ~ less_or_equal(add(additive_identity,additive_inverse(a)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[],[f42,f2]) ).
fof(f74,plain,
( ~ less_or_equal(add(additive_identity,additive_inverse(a)),additive_identity)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f70,f47]) ).
fof(f80,plain,
( ! [X0] :
( ~ less_or_equal(add(additive_identity,additive_inverse(a)),X0)
| ~ less_or_equal(X0,additive_identity) )
| ~ spl0_3 ),
inference(resolution,[],[f74,f17]) ).
fof(f199,plain,
( ! [X0] :
( ~ less_or_equal(add(X0,additive_inverse(a)),additive_identity)
| ~ defined(additive_inverse(a))
| ~ less_or_equal(additive_identity,X0) )
| ~ spl0_3 ),
inference(resolution,[],[f80,f19]) ).
fof(f206,plain,
( ! [X0] :
( ~ less_or_equal(add(X0,additive_inverse(a)),additive_identity)
| ~ less_or_equal(additive_identity,X0) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f199,f47]) ).
fof(f403,plain,
( ! [X0,X1] :
( ~ equalish(X1,add(X0,additive_inverse(a)))
| ~ less_or_equal(X1,additive_identity)
| ~ less_or_equal(additive_identity,X0) )
| ~ spl0_3 ),
inference(resolution,[],[f206,f26]) ).
fof(f1162,plain,
( ! [X0,X1] :
( ~ equalish(add(X1,additive_inverse(a)),X0)
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(X0,additive_identity) )
| ~ spl0_3 ),
inference(resolution,[],[f403,f22]) ).
fof(f2881,plain,
( ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(additive_identity,additive_identity)
| ~ defined(a)
| ~ spl0_3 ),
inference(resolution,[],[f1162,f3]) ).
fof(f2885,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| ~ defined(a)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f2881,f29]) ).
fof(f2887,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f2885,f28]) ).
fof(f2896,plain,
( less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity)
| ~ defined(additive_identity)
| ~ spl0_3 ),
inference(resolution,[],[f2887,f18]) ).
fof(f2897,plain,
( less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity)
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f2896]) ).
fof(f2901,plain,
( ~ defined(additive_identity)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f2897,f2887]) ).
fof(f2902,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f2901,f11]) ).
fof(f2903,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f2902]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f59]) ).
cnf(s69,plain,
~ spl0_3,
inference(sat_conversion,[],[f2903]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s3,s69]) ).
fof(f2904,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD064-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 00:50:22 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 4.48/1.37 % (946861)Input is clausal, will run a generic CNF schedule.
% 4.48/1.37 % (946869)lrs+10_1_sil=8000:sp=occurrence:random_seed=1574130376:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.48/1.37 % (946869)Instruction limit reached!
% 4.48/1.37 % (946869)------------------------------
% 4.48/1.37 % (946869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.48/1.37 % (946869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.48/1.37 % (946869)CaDiCaL version: 2.1.3
% 4.48/1.37 % (946869)Termination reason: Instruction limit
% 4.48/1.37 % (946869)Termination phase: Saturation
% 4.48/1.37 % (946869)Time elapsed: 0.038 s
% 4.48/1.37 % (946869)Peak memory usage: 89 MB
% 4.48/1.37 % (946869)Instructions burned: 111 (million)
% 4.48/1.37 % (946866)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=3905085720:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.48/1.37 % (946868)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3030019110:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.48/1.37 % (946867)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4291520193:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.48/1.37 % (946872)dis-21_1_sil=8000:lcm=predicate:random_seed=4272531105: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)
% 4.48/1.37 % (946870)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=724240618:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.48/1.37 % (946871)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2172795737:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.48/1.37 % (946872)Instruction limit reached!
% 4.48/1.37 % (946872)------------------------------
% 4.48/1.37 % (946872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.48/1.37 % (946872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.48/1.37 % (946872)CaDiCaL version: 2.1.3
% 4.48/1.37 % (946872)Termination reason: Instruction limit
% 4.48/1.37 % (946872)Termination phase: Saturation
% 4.48/1.37 % (946872)Time elapsed: 0.051 s
% 4.48/1.37 % (946872)Peak memory usage: 88 MB
% 4.48/1.37 % (946872)Instructions burned: 118 (million)
% 4.48/1.37 % (946870)Instruction limit reached!
% 4.48/1.37 % (946870)------------------------------
% 4.48/1.37 % (946870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.48/1.37 % (946870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.48/1.37 % (946870)CaDiCaL version: 2.1.3
% 4.48/1.37 % (946870)Termination reason: Instruction limit
% 4.48/1.37 % (946870)Termination phase: Saturation
% 4.48/1.37 % (946870)Time elapsed: 0.068 s
% 4.48/1.37 % (946870)Peak memory usage: 88 MB
% 4.48/1.37 % (946870)Instructions burned: 114 (million)
% 4.48/1.37 % (946877)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=3029116638:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.48/1.37 % (946871)Instruction limit reached!
% 4.48/1.37 % (946871)------------------------------
% 4.48/1.37 % (946871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.48/1.37 % (946871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.48/1.37 % (946871)CaDiCaL version: 2.1.3
% 4.48/1.37 % (946871)Termination reason: Instruction limit
% 4.48/1.37 % (946871)Termination phase: Saturation
% 4.48/1.37 % (946871)Time elapsed: 0.123 s
% 4.48/1.37 % (946871)Peak memory usage: 89 MB
% 4.48/1.37 % (946871)Instructions burned: 180 (million)
% 4.48/1.37 % (946877)Instruction limit reached!
% 4.48/1.37 % (946877)------------------------------
% 4.48/1.37 % (946877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.48/1.37 % (946877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.48/1.37 % (946877)CaDiCaL version: 2.1.3
% 4.48/1.37 % (946877)Termination reason: Instruction limit
% 4.48/1.37 % (946877)Termination phase: Saturation
% 4.48/1.37 % (946877)Time elapsed: 0.035 s
% 4.48/1.37 % (946877)Peak memory usage: 88 MB
% 4.48/1.37 % (946877)Instructions burned: 146 (million)
% 4.48/1.37 % (946881)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=288019057: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)
% 5.53/1.57 % (946882)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=232215979:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.53/1.57 % (946885)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=212987369:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 5.53/1.57 % (946884)lrs+10_64_to=lpo:sil=8000:random_seed=3206972310:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.53/1.57 % (946882)First to succeed.
% 5.53/1.57 % (946882)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-946861"
% 5.53/1.57 % (946881)Instruction limit reached!
% 5.53/1.57 % (946881)------------------------------
% 5.53/1.57 % (946881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.57 % (946881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.57 % (946881)CaDiCaL version: 2.1.3
% 5.53/1.57 % (946881)Termination reason: Instruction limit
% 5.53/1.57 % (946881)Termination phase: Saturation
% 5.53/1.57 % (946881)Time elapsed: 0.098 s
% 5.53/1.57 % (946881)Peak memory usage: 94 MB
% 5.53/1.57 % (946881)Instructions burned: 190 (million)
% 5.53/1.57 % (946885)Instruction limit reached!
% 5.53/1.57 % (946885)------------------------------
% 5.53/1.57 % (946885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.57 % (946885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.57 % (946885)CaDiCaL version: 2.1.3
% 5.53/1.57 % (946885)Termination reason: Instruction limit
% 5.53/1.57 % (946885)Termination phase: Saturation
% 5.53/1.57 % (946885)Time elapsed: 0.073 s
% 5.53/1.57 % (946885)Peak memory usage: 89 MB
% 5.53/1.57 % (946885)Instructions burned: 196 (million)
% 5.53/1.57 % (946884)Instruction limit reached!
% 5.53/1.57 % (946884)------------------------------
% 5.53/1.57 % (946884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.57 % (946884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.57 % (946884)CaDiCaL version: 2.1.3
% 5.53/1.57 % (946884)Termination reason: Instruction limit
% 5.53/1.57 % (946884)Termination phase: Saturation
% 5.53/1.57 % (946884)Time elapsed: 0.080 s
% 5.53/1.57 % (946884)Peak memory usage: 89 MB
% 5.53/1.57 % (946884)Instructions burned: 127 (million)
% 5.53/1.57 % (946890)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2043489154:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.53/1.57 % (946891)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1889349443:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 5.53/1.57 % (946890)Also succeeded, but the first one will report.
% 5.53/1.57 % (946892)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=4093738097:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 5.53/1.57 % (946882)Refutation found. Thanks to Tanya!
% 5.53/1.57 % SZS status Unsatisfiable for theBenchmark
% 5.53/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 5.53/1.57 % (946882)------------------------------
% 5.53/1.57 % (946882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.57 % (946882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.57 % (946882)CaDiCaL version: 2.1.3
% 5.53/1.57 % (946882)Termination reason: Refutation
% 5.53/1.57 % (946882)Time elapsed: 0.049 s
% 5.53/1.57 % (946882)Peak memory usage: 90 MB
% 5.53/1.57 % (946882)Instructions burned: 74 (million)
% 5.53/1.57 % (946882)------------------------------
% 5.53/1.57 % (946882)------------------------------
% 5.53/1.57 % (946861)Success in time 0.694 s
% 5.53/1.57 % Vampire exiting
%------------------------------------------------------------------------------