%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD010-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:48:59 AM UTC 2026
% Result : Unsatisfiable 0.19s 1.03s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 9 unt; 2 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 24 ~; 26 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( equalish(multiply(multiplicative_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f14,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
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(X1,X0)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f27,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
fof(f28,negated_conjecture,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inv_not_equal_to_multiplicative_id_2) ).
fof(f38,plain,
! [X0,X1] :
( ~ equalish(X0,multiply(multiplicative_identity,X1))
| equalish(X0,X1)
| ~ defined(X1) ),
inference(resolution,[],[f23,f6]) ).
fof(f57,plain,
! [X0] :
( equalish(multiplicative_identity,multiply(X0,multiplicative_inverse(X0)))
| equalish(X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[],[f7,f22]) ).
fof(f175,plain,
( equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[],[f57,f38]) ).
fof(f180,plain,
( equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(forward_subsumption_resolution,[],[f175,f15]) ).
fof(f181,plain,
( equalish(multiplicative_identity,additive_identity)
| equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
inference(forward_subsumption_resolution,[],[f180,f14]) ).
fof(f183,definition,
( spl0_5
<=> equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f185,plain,
( equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f187,definition,
( spl0_6
<=> equalish(multiplicative_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f189,plain,
( equalish(multiplicative_identity,additive_identity)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f190,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f181,f187,f183]) ).
fof(f193,plain,
( equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ spl0_5 ),
inference(resolution,[],[f185,f22]) ).
fof(f194,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f193,f28]) ).
fof(f195,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f206,plain,
( equalish(additive_identity,multiplicative_identity)
| ~ spl0_6 ),
inference(resolution,[],[f189,f22]) ).
fof(f207,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f206,f27]) ).
fof(f208,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f207]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f190]) ).
cnf(s5,plain,
~ spl0_5,
inference(sat_conversion,[],[f195]) ).
cnf(s6,plain,
~ spl0_6,
inference(sat_conversion,[],[f208]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s4,s6,s5]) ).
fof(f210,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD010-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n008.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 00:23:25 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 0.19/1.03 % (2810001)Input is clausal, will run a generic CNF schedule.
% 0.19/1.03 % (2810009)lrs+10_1_sil=8000:sp=occurrence:random_seed=1660084333:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.03 % (2810009)First to succeed.
% 0.19/1.03 % (2810009)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2810001"
% 0.19/1.03 % (2810007)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2274266999:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.03 % (2810006)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=1940421696:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.03 % (2810008)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=67292693:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.03 % (2810011)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2812761604:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.03 % (2810012)dis-21_1_sil=8000:lcm=predicate:random_seed=3678732125: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)
% 0.19/1.03 % (2810010)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1650431724:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.03 % (2810011)Also succeeded, but the first one will report.
% 0.19/1.03 % (2810010)Also succeeded, but the first one will report.
% 0.19/1.03 % (2810012)Also succeeded, but the first one will report.
% 0.19/1.03 % (2810009)Refutation found. Thanks to Tanya!
% 0.19/1.03 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.03 % (2810009)------------------------------
% 0.19/1.03 % (2810009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.03 % (2810009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.03 % (2810009)CaDiCaL version: 2.1.3
% 0.19/1.03 % (2810009)Termination reason: Refutation
% 0.19/1.03 % (2810009)Time elapsed: 0.003 s
% 0.19/1.03 % (2810009)Peak memory usage: 89 MB
% 0.19/1.03 % (2810009)Instructions burned: 6 (million)
% 0.19/1.03 % (2810009)------------------------------
% 0.19/1.03 % (2810009)------------------------------
% 0.19/1.03 % (2810001)Success in time 0.269 s
% 0.19/1.03 % Vampire exiting
%------------------------------------------------------------------------------