%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD004-1 : 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 : 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 09:48:57 AM UTC 2026
% Result : Unsatisfiable 3.81s 1.21s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 11 unt; 3 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 113 ( 60 ~; 50 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 22 !; 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(f8,axiom,
! [X0,X1] :
( equalish(multiply(X0,X1),multiply(X1,X0))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f13,axiom,
! [X0,X1] :
( defined(multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_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(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,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_equal_to_additive_identity_3) ).
fof(f31,negated_conjecture,
~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_not_equal_to_a_4) ).
fof(f43,plain,
! [X0] :
( ~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),X0)
| ~ equalish(X0,a) ),
inference(resolution,[],[f23,f31]) ).
fof(f102,plain,
! [X0,X1] :
( ~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),X1)
| ~ equalish(X0,a)
| ~ equalish(X1,X0) ),
inference(resolution,[],[f43,f23]) ).
fof(f105,definition,
( spl0_1
<=> defined(multiply(b,multiplicative_inverse(b))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f106,plain,
( ~ defined(multiply(b,multiplicative_inverse(b)))
| spl0_1 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f119,definition,
( spl0_4
<=> defined(multiplicative_inverse(b)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f120,plain,
( ~ defined(multiplicative_inverse(b))
| spl0_4 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f125,plain,
( ~ defined(b)
| ~ defined(multiplicative_inverse(b))
| spl0_1 ),
inference(resolution,[],[f106,f13]) ).
fof(f126,plain,
( ~ defined(multiplicative_inverse(b))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f125,f29]) ).
fof(f127,plain,
( ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f126,f105,f119]) ).
fof(f131,plain,
( ~ defined(b)
| equalish(b,additive_identity)
| spl0_4 ),
inference(resolution,[],[f120,f15]) ).
fof(f132,plain,
( equalish(b,additive_identity)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f131,f29]) ).
fof(f133,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f132,f30]) ).
fof(f134,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f241,plain,
! [X0] :
( ~ equalish(X0,a)
| ~ equalish(multiply(multiply(b,multiplicative_inverse(b)),a),X0)
| ~ defined(a)
| ~ defined(multiply(b,multiplicative_inverse(b))) ),
inference(resolution,[],[f102,f8]) ).
fof(f252,plain,
! [X0] :
( ~ equalish(X0,a)
| ~ equalish(multiply(multiply(b,multiplicative_inverse(b)),a),X0)
| ~ defined(multiply(b,multiplicative_inverse(b))) ),
inference(forward_subsumption_resolution,[],[f241,f28]) ).
fof(f255,definition,
( spl0_17
<=> ! [X0] :
( ~ equalish(X0,a)
| ~ equalish(multiply(multiply(b,multiplicative_inverse(b)),a),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f256,plain,
( ! [X0] :
( ~ equalish(multiply(multiply(b,multiplicative_inverse(b)),a),X0)
| ~ equalish(X0,a) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( ~ spl0_1
| spl0_17 ),
inference(avatar_split_clause,[],[f252,f255,f105]) ).
fof(f650,plain,
( ! [X0] :
( ~ equalish(multiply(X0,a),a)
| ~ defined(a)
| ~ equalish(multiply(b,multiplicative_inverse(b)),X0) )
| ~ spl0_17 ),
inference(resolution,[],[f256,f25]) ).
fof(f654,plain,
( ! [X0] :
( ~ equalish(multiply(b,multiplicative_inverse(b)),X0)
| ~ equalish(multiply(X0,a),a) )
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f650,f28]) ).
fof(f2850,plain,
( ~ equalish(multiply(multiplicative_identity,a),a)
| ~ defined(b)
| equalish(b,additive_identity)
| ~ spl0_17 ),
inference(resolution,[],[f654,f7]) ).
fof(f2858,plain,
( ~ equalish(multiply(multiplicative_identity,a),a)
| equalish(b,additive_identity)
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f2850,f29]) ).
fof(f2864,plain,
( ~ equalish(multiply(multiplicative_identity,a),a)
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f2858,f30]) ).
fof(f2869,plain,
( ~ defined(a)
| ~ spl0_17 ),
inference(resolution,[],[f2864,f6]) ).
fof(f2872,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f2869,f28]) ).
fof(f2873,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f2872]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f127]) ).
cnf(s5,plain,
spl0_4,
inference(sat_conversion,[],[f134]) ).
cnf(s16,plain,
( ~ spl0_1
| spl0_17 ),
inference(sat_conversion,[],[f257]) ).
cnf(s296,plain,
~ spl0_17,
inference(sat_conversion,[],[f2873]) ).
cnf(s313,plain,
~ spl0_1,
inference(rat,[],[s16,s296]) ).
cnf(s320,plain,
$false,
inference(rat,[],[s4,s5,s313]) ).
fof(f2874,plain,
$false,
inference(avatar_sat_refutation,[],[s320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD004-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n008.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 00:22:54 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running first-order theorem proving
% 0.12/0.23 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
% 3.81/1.21 % (2808749)Input is clausal, will run a generic CNF schedule.
% 3.81/1.21 % (2808878)lrs+10_1_sil=8000:sp=occurrence:random_seed=3316527054:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.81/1.21 % (2808875)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=2064308371:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.81/1.21 % (2808876)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1765238018:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.81/1.21 % (2808878)Instruction limit reached!
% 3.81/1.21 % (2808878)------------------------------
% 3.81/1.21 % (2808878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (2808878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (2808878)CaDiCaL version: 2.1.3
% 3.81/1.21 % (2808878)Termination reason: Instruction limit
% 3.81/1.21 % (2808878)Termination phase: Saturation
% 3.81/1.21 % (2808878)Time elapsed: 0.037 s
% 3.81/1.21 % (2808878)Peak memory usage: 89 MB
% 3.81/1.21 % (2808878)Instructions burned: 107 (million)
% 3.81/1.21 % (2808881)dis-21_1_sil=8000:lcm=predicate:random_seed=3188788595: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)
% 3.81/1.21 % (2808880)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1944233936:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.81/1.21 % (2808879)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3592622234:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.81/1.21 % (2808877)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1365735996:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.81/1.21 % (2808879)First to succeed.
% 3.81/1.21 % (2808879)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2808749"
% 3.81/1.21 % (2808881)Instruction limit reached!
% 3.81/1.21 % (2808881)------------------------------
% 3.81/1.21 % (2808881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (2808881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (2808881)CaDiCaL version: 2.1.3
% 3.81/1.21 % (2808881)Termination reason: Instruction limit
% 3.81/1.21 % (2808881)Termination phase: Saturation
% 3.81/1.21 % (2808881)Time elapsed: 0.075 s
% 3.81/1.21 % (2808881)Peak memory usage: 90 MB
% 3.81/1.21 % (2808881)Instructions burned: 119 (million)
% 3.81/1.21 % (2808885)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=1753883024:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.81/1.21 % (2808885)Refutation not found, incomplete strategy
% 3.81/1.21 % (2808885)------------------------------
% 3.81/1.21 % (2808885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (2808885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (2808885)CaDiCaL version: 2.1.3
% 3.81/1.21 % (2808885)Termination reason: Refutation not found, incomplete strategy
% 3.81/1.21 % (2808885)Time elapsed: 0.0000 s
% 3.81/1.21 % (2808885)Peak memory usage: 87 MB
% 3.81/1.21 % (2808880)Instruction limit reached!
% 3.81/1.21 % (2808880)------------------------------
% 3.81/1.21 % (2808880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (2808880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (2808880)CaDiCaL version: 2.1.3
% 3.81/1.21 % (2808880)Termination reason: Instruction limit
% 3.81/1.21 % (2808880)Termination phase: Saturation
% 3.81/1.21 % (2808880)Time elapsed: 0.118 s
% 3.81/1.21 % (2808880)Peak memory usage: 89 MB
% 3.81/1.21 % (2808880)Instructions burned: 181 (million)
% 3.81/1.21 % (2808890)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3483780305: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)
% 3.81/1.21 % (2808885)------------------------------
% 3.81/1.21 % (2808885)------------------------------
% 3.81/1.21 % (2808892)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=172255674:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.81/1.21 % (2808892)Also succeeded, but the first one will report.
% 3.81/1.21 % (2808890)Instruction limit reached!
% 3.81/1.21 % (2808890)------------------------------
% 3.81/1.21 % (2808890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (2808890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (2808890)CaDiCaL version: 2.1.3
% 3.81/1.21 % (2808890)Termination reason: Instruction limit
% 3.81/1.21 % (2808890)Termination phase: Saturation
% 3.81/1.21 % (2808890)Time elapsed: 0.098 s
% 3.81/1.21 % (2808890)Peak memory usage: 94 MB
% 3.81/1.21 % (2808890)Instructions burned: 190 (million)
% 3.81/1.21 % (2808879)Refutation found. Thanks to Tanya!
% 3.81/1.21 % SZS status Unsatisfiable for theBenchmark
% 3.81/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.21 % (2808879)------------------------------
% 3.81/1.21 % (2808879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (2808879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (2808879)CaDiCaL version: 2.1.3
% 3.81/1.21 % (2808879)Termination reason: Refutation
% 3.81/1.21 % (2808879)Time elapsed: 0.058 s
% 3.81/1.21 % (2808879)Peak memory usage: 90 MB
% 3.81/1.21 % (2808879)Instructions burned: 93 (million)
% 3.81/1.21 % (2808879)------------------------------
% 3.81/1.21 % (2808879)------------------------------
% 3.81/1.21 % (2808749)Success in time 0.449 s
% 3.81/1.21 % Vampire exiting
%------------------------------------------------------------------------------