%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD037-1 : 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 : n012.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 09:49:08 AM UTC 2026
% Result : Unsatisfiable 2.14s 0.71s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 12 unt; 2 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 37 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity)
| ~ defined(X0)
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f15,axiom,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
fof(f22,axiom,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f30,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
fof(f31,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_4) ).
fof(f32,negated_conjecture,
~ equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity_not_equal_to_multiply_5) ).
fof(f34,plain,
~ equalish(multiply(b,multiplicative_inverse(a)),multiplicative_identity),
inference(resolution,[],[f22,f32]) ).
fof(f44,plain,
! [X0] :
( ~ equalish(multiply(b,multiplicative_inverse(a)),X0)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[],[f23,f34]) ).
fof(f111,definition,
( spl0_3
<=> defined(multiplicative_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f112,plain,
( ~ defined(multiplicative_inverse(a))
| spl0_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f126,plain,
( ~ defined(a)
| equalish(a,additive_identity)
| spl0_3 ),
inference(resolution,[],[f112,f15]) ).
fof(f127,plain,
( equalish(a,additive_identity)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f126,f28]) ).
fof(f128,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f127,f30]) ).
fof(f129,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f128]) ).
fof(f178,plain,
! [X0] :
( ~ equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)
| ~ defined(multiplicative_inverse(a))
| ~ equalish(b,X0) ),
inference(resolution,[],[f44,f25]) ).
fof(f183,definition,
( spl0_7
<=> ! [X0] :
( ~ equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)
| ~ equalish(b,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f184,plain,
( ! [X0] :
( ~ equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)
| ~ equalish(b,X0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f185,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f178,f183,f111]) ).
fof(f547,plain,
( ~ equalish(b,a)
| ~ defined(a)
| equalish(a,additive_identity)
| ~ spl0_7 ),
inference(resolution,[],[f184,f7]) ).
fof(f551,plain,
( ~ equalish(b,a)
| equalish(a,additive_identity)
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f547,f28]) ).
fof(f552,plain,
( ~ equalish(b,a)
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f551,f30]) ).
fof(f554,plain,
( ~ equalish(a,b)
| ~ spl0_7 ),
inference(resolution,[],[f552,f22]) ).
fof(f555,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f554,f31]) ).
fof(f556,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f555]) ).
cnf(s5,plain,
spl0_3,
inference(sat_conversion,[],[f129]) ).
cnf(s7,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f185]) ).
cnf(s28,plain,
~ spl0_7,
inference(sat_conversion,[],[f556]) ).
cnf(s33,plain,
~ spl0_3,
inference(rat,[],[s7,s28]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s5,s33]) ).
fof(f557,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD037-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 00:33:20 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running first-order theorem proving
% 0.09/0.13 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
% 2.14/0.71 % (3950277)Input is clausal, will run a generic CNF schedule.
% 2.14/0.71 % (3950332)dis-21_1_sil=8000:lcm=predicate:random_seed=2896981314:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 2.14/0.71 % (3950330)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1194025209:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 2.14/0.71 % (3950324)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=58097798:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 2.14/0.71 % (3950327)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=87005405:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 2.14/0.71 % (3950328)lrs+10_1_sil=8000:sp=occurrence:random_seed=3223671538:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 2.14/0.71 % (3950326)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2511000963:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 2.14/0.71 % (3950330)First to succeed.
% 2.14/0.71 % (3950330)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3950277"
% 2.14/0.71 % (3950331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1993055370:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 2.14/0.71 % (3950331)Also succeeded, but the first one will report.
% 2.14/0.71 % (3950328)Also succeeded, but the first one will report.
% 2.14/0.71 % (3950332)Also succeeded, but the first one will report.
% 2.14/0.71 % (3950330)Refutation found. Thanks to Tanya!
% 2.14/0.71 % SZS status Unsatisfiable for theBenchmark
% 2.14/0.71 % SZS output start Proof for theBenchmark
% See solution above
% 2.14/0.71 % (3950330)------------------------------
% 2.14/0.71 % (3950330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/0.71 % (3950330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.71 % (3950330)CaDiCaL version: 2.1.3
% 2.14/0.71 % (3950330)Termination reason: Refutation
% 2.14/0.71 % (3950330)Time elapsed: 0.006 s
% 2.14/0.71 % (3950330)Peak memory usage: 88 MB
% 2.14/0.71 % (3950330)Instructions burned: 13 (million)
% 2.14/0.71 % (3950330)------------------------------
% 2.14/0.71 % (3950330)------------------------------
% 2.14/0.71 % (3950277)Success in time 0.26 s
% 2.14/0.71 % Vampire exiting
%------------------------------------------------------------------------------