%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD031-1 : 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 : 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 09:49:06 AM UTC 2026
% Result : Unsatisfiable 4.98s 1.47s
% Output : Refutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 10 unt; 1 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 43 ~; 35 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( equalish(multiply(multiplicative_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f7,axiom,
! [X0] :
( equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity)
| ~ defined(X0)
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f15,axiom,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_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(f25,axiom,
! [X2,X0,X1] :
( equalish(multiply(X0,X1),multiply(X2,X1))
| ~ defined(X1)
| ~ equalish(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,negated_conjecture,
equalish(a,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_multiplicative_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(f31,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverses_not_equal) ).
fof(f37,plain,
! [X0] :
( ~ equalish(multiplicative_inverse(a),X0)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[],[f31,f23]) ).
fof(f45,plain,
! [X0] :
( ~ equalish(X0,multiplicative_inverse(a))
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[],[f37,f22]) ).
fof(f65,definition,
( spl0_1
<=> defined(multiplicative_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f66,plain,
( defined(multiplicative_inverse(a))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f67,plain,
( ~ defined(multiplicative_inverse(a))
| spl0_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f78,plain,
( ~ defined(a)
| equalish(a,additive_identity)
| spl0_1 ),
inference(resolution,[],[f67,f15]) ).
fof(f79,plain,
( equalish(a,additive_identity)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f78,f28]) ).
fof(f80,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f79,f30]) ).
fof(f81,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f86,plain,
( ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[],[f45,f6]) ).
fof(f87,plain,
( ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_identity)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f86,f66]) ).
fof(f116,plain,
( ! [X0] :
( ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),X0)
| ~ equalish(X0,multiplicative_identity) )
| ~ spl0_1 ),
inference(resolution,[],[f87,f23]) ).
fof(f325,plain,
( ! [X0] :
( ~ equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)
| ~ defined(multiplicative_inverse(a))
| ~ equalish(multiplicative_identity,X0) )
| ~ spl0_1 ),
inference(resolution,[],[f116,f25]) ).
fof(f332,plain,
( ! [X0] :
( ~ equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)
| ~ equalish(multiplicative_identity,X0) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f325,f66]) ).
fof(f598,plain,
( ~ equalish(multiplicative_identity,a)
| ~ defined(a)
| equalish(a,additive_identity)
| ~ spl0_1 ),
inference(resolution,[],[f332,f7]) ).
fof(f601,plain,
( ~ equalish(multiplicative_identity,a)
| equalish(a,additive_identity)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f598,f28]) ).
fof(f602,plain,
( ~ equalish(multiplicative_identity,a)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f601,f30]) ).
fof(f603,plain,
( ~ equalish(a,multiplicative_identity)
| ~ spl0_1 ),
inference(resolution,[],[f602,f22]) ).
fof(f605,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f603,f29]) ).
fof(f606,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f605]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f81]) ).
cnf(s16,plain,
~ spl0_1,
inference(sat_conversion,[],[f606]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s3,s16]) ).
fof(f607,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD031-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:35:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.98/1.47 % (10723)Input is clausal, will run a generic CNF schedule.
% 4.98/1.47 % (10732)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3852693736:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.98/1.47 % (10732)Instruction limit reached!
% 4.98/1.47 % (10732)------------------------------
% 4.98/1.47 % (10732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.47 % (10732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.47 % (10732)CaDiCaL version: 2.1.3
% 4.98/1.47 % (10732)Termination reason: Instruction limit
% 4.98/1.47 % (10732)Termination phase: Saturation
% 4.98/1.47 % (10732)Time elapsed: 0.039 s
% 4.98/1.47 % (10732)Peak memory usage: 88 MB
% 4.98/1.47 % (10732)Instructions burned: 116 (million)
% 4.98/1.47 % (10733)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3332858524:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.98/1.47 % (10730)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2538966831:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.98/1.47 % (10731)lrs+10_1_sil=8000:sp=occurrence:random_seed=371685445:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.98/1.47 % (10728)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=567370841:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.98/1.47 % (10729)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=355092236:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.98/1.47 % (10734)dis-21_1_sil=8000:lcm=predicate:random_seed=3729467088: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)
% 4.98/1.47 % (10731)Instruction limit reached!
% 4.98/1.47 % (10731)------------------------------
% 4.98/1.47 % (10731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.47 % (10731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.47 % (10731)CaDiCaL version: 2.1.3
% 4.98/1.47 % (10731)Termination reason: Instruction limit
% 4.98/1.47 % (10731)Termination phase: Saturation
% 4.98/1.47 % (10731)Time elapsed: 0.068 s
% 4.98/1.47 % (10731)Peak memory usage: 89 MB
% 4.98/1.47 % (10731)Instructions burned: 108 (million)
% 4.98/1.47 % (10734)Instruction limit reached!
% 4.98/1.47 % (10734)------------------------------
% 4.98/1.47 % (10734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.47 % (10734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.47 % (10734)CaDiCaL version: 2.1.3
% 4.98/1.47 % (10734)Termination reason: Instruction limit
% 4.98/1.47 % (10734)Termination phase: Saturation
% 4.98/1.47 % (10734)Time elapsed: 0.074 s
% 4.98/1.47 % (10734)Peak memory usage: 89 MB
% 4.98/1.47 % (10734)Instructions burned: 117 (million)
% 4.98/1.47 % (10736)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=3685336631:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.98/1.47 % (10733)Instruction limit reached!
% 4.98/1.47 % (10733)------------------------------
% 4.98/1.47 % (10733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.47 % (10733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.47 % (10733)CaDiCaL version: 2.1.3
% 4.98/1.47 % (10733)Termination reason: Instruction limit
% 4.98/1.47 % (10733)Termination phase: Saturation
% 4.98/1.47 % (10733)Time elapsed: 0.119 s
% 4.98/1.47 % (10733)Peak memory usage: 89 MB
% 4.98/1.47 % (10733)Instructions burned: 181 (million)
% 4.98/1.47 % (10736)Instruction limit reached!
% 4.98/1.47 % (10736)------------------------------
% 4.98/1.47 % (10736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.47 % (10736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.47 % (10736)CaDiCaL version: 2.1.3
% 4.98/1.47 % (10736)Termination reason: Instruction limit
% 4.98/1.47 % (10736)Termination phase: Saturation
% 4.98/1.47 % (10736)Time elapsed: 0.046 s
% 4.98/1.47 % (10736)Peak memory usage: 89 MB
% 4.98/1.47 % (10736)Instructions burned: 146 (million)
% 4.98/1.47 % (10745)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4210441300:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.98/1.47 % (10743)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3071288940: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)
% 4.98/1.47 % (10747)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=157376183:avsq=on:i=194:fgj=on:bd=preordered_2997 on theBenchmark for (2997ds/194Mi)
% 4.98/1.47 % (10745)First to succeed.
% 4.98/1.47 % (10745)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10723"
% 4.98/1.47 % (10747)Also succeeded, but the first one will report.
% 4.98/1.47 % (10746)lrs+10_64_to=lpo:sil=8000:random_seed=787615578:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.98/1.47 % (10743)Instruction limit reached!
% 4.98/1.47 % (10743)------------------------------
% 4.98/1.47 % (10743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.47 % (10743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.47 % (10743)CaDiCaL version: 2.1.3
% 4.98/1.47 % (10743)Termination reason: Instruction limit
% 4.98/1.47 % (10743)Termination phase: Saturation
% 4.98/1.47 % (10743)Time elapsed: 0.097 s
% 4.98/1.47 % (10743)Peak memory usage: 94 MB
% 4.98/1.47 % (10743)Instructions burned: 189 (million)
% 4.98/1.47 % (10746)Instruction limit reached!
% 4.98/1.47 % (10746)------------------------------
% 4.98/1.47 % (10746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.47 % (10746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.47 % (10746)CaDiCaL version: 2.1.3
% 4.98/1.47 % (10746)Termination reason: Instruction limit
% 4.98/1.47 % (10746)Termination phase: Saturation
% 4.98/1.47 % (10746)Time elapsed: 0.074 s
% 4.98/1.47 % (10746)Peak memory usage: 89 MB
% 4.98/1.47 % (10746)Instructions burned: 128 (million)
% 4.98/1.47 % (10752)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1884079984:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 4.98/1.47 % (10753)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3798285034:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 4.98/1.47 % (10745)Refutation found. Thanks to Tanya!
% 4.98/1.47 % SZS status Unsatisfiable for theBenchmark
% 4.98/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 4.98/1.47 % (10745)------------------------------
% 4.98/1.47 % (10745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.47 % (10745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.47 % (10745)CaDiCaL version: 2.1.3
% 4.98/1.47 % (10745)Termination reason: Refutation
% 4.98/1.47 % (10745)Time elapsed: 0.012 s
% 4.98/1.47 % (10745)Peak memory usage: 89 MB
% 4.98/1.47 % (10745)Instructions burned: 15 (million)
% 4.98/1.47 % (10745)------------------------------
% 4.98/1.47 % (10745)------------------------------
% 4.98/1.47 % (10723)Success in time 0.616 s
% 4.98/1.47 % Vampire exiting
%------------------------------------------------------------------------------