%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD019-1 : 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 : 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 09:49:02 AM UTC 2026
% Result : Unsatisfiable 5.42s 1.54s
% Output : Refutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 42 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 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(f4,axiom,
! [X0,X1] :
( equalish(add(X0,X1),add(X1,X0))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f12,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f22,axiom,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,negated_conjecture,
equalish(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_equals_additive_identity_2) ).
fof(f30,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
fof(f32,plain,
! [X0] :
( ~ equalish(a,X0)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[],[f30,f23]) ).
fof(f36,plain,
! [X0] :
( ~ equalish(X0,a)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[],[f32,f22]) ).
fof(f44,plain,
( ~ equalish(add(additive_identity,a),additive_identity)
| ~ defined(a) ),
inference(resolution,[],[f36,f2]) ).
fof(f47,plain,
~ equalish(add(additive_identity,a),additive_identity),
inference(forward_subsumption_resolution,[],[f44,f28]) ).
fof(f56,plain,
! [X0] :
( ~ equalish(add(additive_identity,a),X0)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[],[f47,f23]) ).
fof(f100,plain,
! [X0] :
( ~ equalish(add(X0,a),additive_identity)
| ~ defined(a)
| ~ equalish(additive_identity,X0) ),
inference(resolution,[],[f56,f24]) ).
fof(f106,plain,
! [X0] :
( ~ equalish(add(X0,a),additive_identity)
| ~ equalish(additive_identity,X0) ),
inference(forward_subsumption_resolution,[],[f100,f28]) ).
fof(f241,plain,
! [X0,X1] :
( ~ equalish(add(X0,a),X1)
| ~ equalish(additive_identity,X0)
| ~ equalish(X1,additive_identity) ),
inference(resolution,[],[f106,f23]) ).
fof(f641,plain,
! [X0] :
( ~ equalish(additive_identity,X0)
| ~ equalish(add(a,X0),additive_identity)
| ~ defined(X0)
| ~ defined(a) ),
inference(resolution,[],[f241,f4]) ).
fof(f645,plain,
! [X0] :
( ~ equalish(add(a,X0),additive_identity)
| ~ equalish(additive_identity,X0)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[],[f641,f28]) ).
fof(f1060,plain,
( ~ equalish(additive_identity,additive_inverse(a))
| ~ defined(additive_inverse(a))
| ~ defined(a) ),
inference(resolution,[],[f645,f3]) ).
fof(f1063,plain,
( ~ equalish(additive_identity,additive_inverse(a))
| ~ defined(a) ),
inference(forward_subsumption_resolution,[],[f1060,f12]) ).
fof(f1064,plain,
~ equalish(additive_identity,additive_inverse(a)),
inference(forward_subsumption_resolution,[],[f1063,f28]) ).
fof(f1067,plain,
~ equalish(additive_inverse(a),additive_identity),
inference(resolution,[],[f1064,f22]) ).
fof(f1069,plain,
$false,
inference(forward_subsumption_resolution,[],[f1067,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD019-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 00:28:03 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 5.42/1.54 % (422595)Input is clausal, will run a generic CNF schedule.
% 5.42/1.54 % (422603)lrs+10_1_sil=8000:sp=occurrence:random_seed=1865824063:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.42/1.54 % (422603)Instruction limit reached!
% 5.42/1.54 % (422603)------------------------------
% 5.42/1.54 % (422603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.54 % (422603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.54 % (422603)CaDiCaL version: 2.1.3
% 5.42/1.54 % (422603)Termination reason: Instruction limit
% 5.42/1.54 % (422603)Termination phase: Saturation
% 5.42/1.54 % (422603)Time elapsed: 0.037 s
% 5.42/1.54 % (422603)Peak memory usage: 89 MB
% 5.42/1.54 % (422603)Instructions burned: 108 (million)
% 5.42/1.54 % (422605)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=103141470:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.42/1.54 % (422602)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1239763589:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.42/1.54 % (422601)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2862708815:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.42/1.54 % (422600)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=2873761869:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.42/1.54 % (422604)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3586592384:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.42/1.54 % (422606)dis-21_1_sil=8000:lcm=predicate:random_seed=462307255: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)
% 5.42/1.54 % (422604)Instruction limit reached!
% 5.42/1.54 % (422604)------------------------------
% 5.42/1.54 % (422604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.54 % (422604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.54 % (422604)CaDiCaL version: 2.1.3
% 5.42/1.54 % (422604)Termination reason: Instruction limit
% 5.42/1.54 % (422604)Termination phase: Saturation
% 5.42/1.54 % (422604)Time elapsed: 0.069 s
% 5.42/1.54 % (422604)Peak memory usage: 88 MB
% 5.42/1.54 % (422604)Instructions burned: 116 (million)
% 5.42/1.54 % (422606)Instruction limit reached!
% 5.42/1.54 % (422606)------------------------------
% 5.42/1.54 % (422606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.54 % (422606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.54 % (422606)CaDiCaL version: 2.1.3
% 5.42/1.54 % (422606)Termination reason: Instruction limit
% 5.42/1.54 % (422606)Termination phase: Saturation
% 5.42/1.54 % (422606)Time elapsed: 0.075 s
% 5.42/1.54 % (422606)Peak memory usage: 89 MB
% 5.42/1.54 % (422606)Instructions burned: 117 (million)
% 5.42/1.54 % (422608)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=1503501387:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.42/1.54 % (422605)Instruction limit reached!
% 5.42/1.54 % (422605)------------------------------
% 5.42/1.54 % (422605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.54 % (422605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.54 % (422605)CaDiCaL version: 2.1.3
% 5.42/1.54 % (422605)Termination reason: Instruction limit
% 5.42/1.54 % (422605)Termination phase: Saturation
% 5.42/1.54 % (422605)Time elapsed: 0.122 s
% 5.42/1.54 % (422605)Peak memory usage: 89 MB
% 5.42/1.54 % (422605)Instructions burned: 180 (million)
% 5.42/1.54 % (422608)Instruction limit reached!
% 5.42/1.54 % (422608)------------------------------
% 5.42/1.54 % (422608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.54 % (422608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.54 % (422608)CaDiCaL version: 2.1.3
% 5.42/1.54 % (422608)Termination reason: Instruction limit
% 5.42/1.54 % (422608)Termination phase: Saturation
% 5.42/1.54 % (422608)Time elapsed: 0.044 s
% 5.42/1.54 % (422608)Peak memory usage: 89 MB
% 5.42/1.54 % (422608)Instructions burned: 146 (million)
% 5.42/1.54 % (422615)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=417469821: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)
% 5.42/1.54 % (422616)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4120509814:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.42/1.54 % (422616)First to succeed.
% 5.42/1.54 % (422616)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-422595"
% 5.42/1.54 % (422619)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2691950346:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 5.42/1.54 % (422618)lrs+10_64_to=lpo:sil=8000:random_seed=1165742627:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.42/1.54 % (422615)Instruction limit reached!
% 5.42/1.54 % (422615)------------------------------
% 5.42/1.54 % (422615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.54 % (422615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.54 % (422615)CaDiCaL version: 2.1.3
% 5.42/1.54 % (422615)Termination reason: Instruction limit
% 5.42/1.54 % (422615)Termination phase: Saturation
% 5.42/1.54 % (422615)Time elapsed: 0.098 s
% 5.42/1.54 % (422615)Peak memory usage: 94 MB
% 5.42/1.54 % (422615)Instructions burned: 190 (million)
% 5.42/1.54 % (422619)Also succeeded, but the first one will report.
% 5.42/1.54 % (422618)Instruction limit reached!
% 5.42/1.54 % (422618)------------------------------
% 5.42/1.54 % (422618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.54 % (422618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.54 % (422618)CaDiCaL version: 2.1.3
% 5.42/1.54 % (422618)Termination reason: Instruction limit
% 5.42/1.54 % (422618)Termination phase: Saturation
% 5.42/1.54 % (422618)Time elapsed: 0.076 s
% 5.42/1.54 % (422618)Peak memory usage: 90 MB
% 5.42/1.54 % (422618)Instructions burned: 126 (million)
% 5.42/1.54 % (422624)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1935025683:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.42/1.54 % (422616)Refutation found. Thanks to Tanya!
% 5.42/1.54 % SZS status Unsatisfiable for theBenchmark
% 5.42/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.42/1.54 % (422616)------------------------------
% 5.42/1.54 % (422616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.54 % (422616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.54 % (422616)CaDiCaL version: 2.1.3
% 5.42/1.54 % (422616)Termination reason: Refutation
% 5.42/1.54 % (422616)Time elapsed: 0.022 s
% 5.42/1.54 % (422616)Peak memory usage: 88 MB
% 5.42/1.54 % (422616)Instructions burned: 34 (million)
% 5.42/1.54 % (422616)------------------------------
% 5.42/1.54 % (422616)------------------------------
% 5.42/1.54 % (422595)Success in time 0.676 s
% 5.42/1.54 % Vampire exiting
%------------------------------------------------------------------------------