%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD010-5 : 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 : n002.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 3.72s 1.27s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 11 unt; 1 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 38 ~; 41 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f9,axiom,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2)
| ~ product(X3,X6,X0)
| ~ product(X4,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_1) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
fof(f27,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_1) ).
fof(f28,negated_conjecture,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
fof(f31,plain,
! [X0] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(resolution,[],[f10,f8]) ).
fof(f74,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X0,X1,multiplicative_inverse(X2))
| sum(X3,X4,multiplicative_identity)
| ~ product(X0,X2,X3)
| ~ product(X1,X2,X4)
| sum(additive_identity,X2,additive_identity)
| ~ defined(X2) ),
inference(resolution,[],[f11,f9]) ).
fof(f282,plain,
! [X2,X0,X1] :
( sum(X0,X1,multiplicative_identity)
| ~ product(additive_identity,X2,X0)
| ~ product(multiplicative_inverse(X2),X2,X1)
| sum(additive_identity,X2,additive_identity)
| ~ defined(X2)
| ~ defined(multiplicative_inverse(X2)) ),
inference(resolution,[],[f74,f3]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ product(multiplicative_inverse(X2),X2,X1)
| ~ product(additive_identity,X2,X0)
| sum(X0,X1,multiplicative_identity)
| sum(additive_identity,X2,additive_identity)
| ~ defined(X2) ),
inference(forward_subsumption_resolution,[],[f282,f18]) ).
fof(f1160,plain,
! [X0] :
( ~ product(additive_identity,multiplicative_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(resolution,[],[f293,f31]) ).
fof(f1180,plain,
! [X0] :
( ~ product(additive_identity,multiplicative_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(forward_subsumption_resolution,[],[f1160,f18]) ).
fof(f1187,plain,
! [X0] :
( ~ product(additive_identity,multiplicative_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(forward_subsumption_resolution,[],[f1180,f27]) ).
fof(f1195,plain,
! [X0] :
( sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ product(additive_identity,multiplicative_identity,X0) ),
inference(forward_subsumption_resolution,[],[f1187,f17]) ).
fof(f1440,definition,
( spl0_37
<=> product(additive_identity,multiplicative_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f1441,plain,
( product(additive_identity,multiplicative_identity,additive_identity)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f1442,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| spl0_37 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f1471,plain,
( ~ defined(additive_identity)
| spl0_37 ),
inference(resolution,[],[f1442,f31]) ).
fof(f1472,plain,
( $false
| spl0_37 ),
inference(forward_subsumption_resolution,[],[f1471,f14]) ).
fof(f1473,plain,
spl0_37,
inference(avatar_contradiction_clause,[],[f1472]) ).
fof(f1483,plain,
~ product(additive_identity,multiplicative_identity,additive_identity),
inference(resolution,[],[f1195,f28]) ).
fof(f1486,plain,
( $false
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1483,f1441]) ).
fof(f1487,plain,
~ spl0_37,
inference(avatar_contradiction_clause,[],[f1486]) ).
cnf(s46,plain,
spl0_37,
inference(sat_conversion,[],[f1473]) ).
cnf(s47,plain,
~ spl0_37,
inference(sat_conversion,[],[f1487]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s46,s47]) ).
fof(f1494,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD010-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 00:25:23 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 3.72/1.27 % (936796)Input is clausal, will run a generic CNF schedule.
% 3.72/1.27 % (936805)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1275611685:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.72/1.27 % (936801)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=302929960:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.72/1.27 % (936806)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1323861984:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.72/1.27 % (936802)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=369068691:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.72/1.27 % (936804)lrs+10_1_sil=8000:sp=occurrence:random_seed=954858059:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.72/1.27 % (936803)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3772185827:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.72/1.27 % (936805)Instruction limit reached!
% 3.72/1.27 % (936805)------------------------------
% 3.72/1.27 % (936805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.27 % (936805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.27 % (936805)CaDiCaL version: 2.1.3
% 3.72/1.27 % (936805)Termination reason: Instruction limit
% 3.72/1.27 % (936805)Termination phase: Saturation
% 3.72/1.27 % (936805)Time elapsed: 0.033 s
% 3.72/1.27 % (936805)Peak memory usage: 88 MB
% 3.72/1.27 % (936805)Instructions burned: 114 (million)
% 3.72/1.27 % (936807)dis-21_1_sil=8000:lcm=predicate:random_seed=2505708419: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)
% 3.72/1.27 % (936804)First to succeed.
% 3.72/1.27 % (936804)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-936796"
% 3.72/1.27 % (936807)Instruction limit reached!
% 3.72/1.27 % (936807)------------------------------
% 3.72/1.27 % (936807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.27 % (936807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.27 % (936807)CaDiCaL version: 2.1.3
% 3.72/1.27 % (936807)Termination reason: Instruction limit
% 3.72/1.27 % (936807)Termination phase: Saturation
% 3.72/1.27 % (936807)Time elapsed: 0.076 s
% 3.72/1.27 % (936807)Peak memory usage: 89 MB
% 3.72/1.27 % (936807)Instructions burned: 118 (million)
% 3.72/1.27 % (936814)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=3640116462:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.72/1.27 % (936806)Instruction limit reached!
% 3.72/1.27 % (936806)------------------------------
% 3.72/1.27 % (936806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.27 % (936806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.27 % (936806)CaDiCaL version: 2.1.3
% 3.72/1.27 % (936806)Termination reason: Instruction limit
% 3.72/1.27 % (936806)Termination phase: Saturation
% 3.72/1.27 % (936806)Time elapsed: 0.106 s
% 3.72/1.27 % (936806)Peak memory usage: 88 MB
% 3.72/1.27 % (936806)Instructions burned: 180 (million)
% 3.72/1.27 % (936814)Instruction limit reached!
% 3.72/1.27 % (936814)------------------------------
% 3.72/1.27 % (936814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.27 % (936814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.27 % (936814)CaDiCaL version: 2.1.3
% 3.72/1.27 % (936814)Termination reason: Instruction limit
% 3.72/1.27 % (936814)Termination phase: Saturation
% 3.72/1.27 % (936814)Time elapsed: 0.031 s
% 3.72/1.27 % (936814)Peak memory usage: 87 MB
% 3.72/1.27 % (936814)Instructions burned: 149 (million)
% 3.72/1.27 % (936819)lrs+10_64_to=lpo:sil=8000:random_seed=3844692879:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 3.72/1.27 % (936817)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3519961153: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)
% 3.72/1.27 % (936817)Also succeeded, but the first one will report.
% 3.72/1.27 % (936818)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3777600096:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.72/1.27 % (936819)Instruction limit reached!
% 3.72/1.27 % (936819)------------------------------
% 3.72/1.27 % (936819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.27 % (936819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.27 % (936819)CaDiCaL version: 2.1.3
% 3.72/1.27 % (936819)Termination reason: Instruction limit
% 3.72/1.27 % (936819)Termination phase: Saturation
% 3.72/1.27 % (936819)Time elapsed: 0.043 s
% 3.72/1.27 % (936819)Peak memory usage: 89 MB
% 3.72/1.27 % (936819)Instructions burned: 127 (million)
% 3.72/1.27 % (936804)Refutation found. Thanks to Tanya!
% 3.72/1.27 % SZS status Unsatisfiable for theBenchmark
% 3.72/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.27 % (936804)------------------------------
% 3.72/1.27 % (936804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.27 % (936804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.27 % (936804)CaDiCaL version: 2.1.3
% 3.72/1.27 % (936804)Termination reason: Refutation
% 3.72/1.27 % (936804)Time elapsed: 0.042 s
% 3.72/1.27 % (936804)Peak memory usage: 89 MB
% 3.72/1.27 % (936804)Instructions burned: 64 (million)
% 3.72/1.27 % (936804)------------------------------
% 3.72/1.27 % (936804)------------------------------
% 3.72/1.27 % (936796)Success in time 0.442 s
% 3.72/1.27 % Vampire exiting
%------------------------------------------------------------------------------