%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD027-3 : 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 09:49:05 AM UTC 2026
% Result : Unsatisfiable 3.70s 1.27s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 23 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication_1) ).
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(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).
fof(f31,negated_conjecture,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_5) ).
fof(f32,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_6) ).
fof(f35,plain,
product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(b)),
inference(resolution,[],[f10,f31]) ).
fof(f43,plain,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f9,f10]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ product(X1,X2,X3)
| ~ product(X0,X1,multiplicative_identity)
| product(X0,X3,X2)
| ~ defined(X2) ),
inference(resolution,[],[f6,f8]) ).
fof(f203,plain,
! [X0] :
( ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| product(X0,multiplicative_inverse(b),multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[],[f55,f35]) ).
fof(f204,plain,
! [X0,X1] :
( ~ product(X0,multiplicative_inverse(X1),multiplicative_identity)
| product(X0,multiplicative_identity,X1)
| ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(resolution,[],[f55,f9]) ).
fof(f211,plain,
! [X0,X1] :
( ~ product(X0,multiplicative_inverse(X1),multiplicative_identity)
| product(X0,multiplicative_identity,X1)
| ~ defined(X1)
| sum(additive_identity,X1,additive_identity) ),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f216,plain,
! [X0] :
( ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| product(X0,multiplicative_inverse(b),multiplicative_identity) ),
inference(forward_subsumption_resolution,[],[f203,f17]) ).
fof(f524,plain,
( product(a,multiplicative_inverse(b),multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[],[f216,f43]) ).
fof(f537,plain,
( product(a,multiplicative_inverse(b),multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(forward_subsumption_resolution,[],[f524,f27]) ).
fof(f538,plain,
product(a,multiplicative_inverse(b),multiplicative_identity),
inference(forward_subsumption_resolution,[],[f537,f29]) ).
fof(f1371,plain,
( product(a,multiplicative_identity,b)
| ~ defined(b)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[],[f211,f538]) ).
fof(f1373,plain,
( product(a,multiplicative_identity,b)
| sum(additive_identity,b,additive_identity) ),
inference(forward_subsumption_resolution,[],[f1371,f28]) ).
fof(f1377,plain,
product(a,multiplicative_identity,b),
inference(forward_subsumption_resolution,[],[f1373,f30]) ).
fof(f1385,plain,
product(multiplicative_identity,a,b),
inference(resolution,[],[f1377,f10]) ).
fof(f1397,plain,
$false,
inference(forward_subsumption_resolution,[],[f1385,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD027-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 00:31:37 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 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
% 3.70/1.27 % (939411)Input is clausal, will run a generic CNF schedule.
% 3.70/1.27 % (939420)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3644089389:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.70/1.27 % (939421)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2907610749:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.70/1.27 % (939417)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=810930458:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.70/1.27 % (939419)lrs+10_1_sil=8000:sp=occurrence:random_seed=1899513117:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.70/1.27 % (939416)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=3803704963:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.70/1.27 % (939418)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=709563455:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.70/1.27 % (939422)dis-21_1_sil=8000:lcm=predicate:random_seed=4052050029: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)
% 3.70/1.27 % (939420)Instruction limit reached!
% 3.70/1.27 % (939420)------------------------------
% 3.70/1.27 % (939420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.27 % (939420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.27 % (939420)CaDiCaL version: 2.1.3
% 3.70/1.27 % (939420)Termination reason: Instruction limit
% 3.70/1.27 % (939420)Termination phase: Saturation
% 3.70/1.27 % (939420)Time elapsed: 0.036 s
% 3.70/1.27 % (939420)Peak memory usage: 88 MB
% 3.70/1.27 % (939420)Instructions burned: 115 (million)
% 3.70/1.27 % (939419)First to succeed.
% 3.70/1.27 % (939419)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-939411"
% 3.70/1.27 % (939422)Instruction limit reached!
% 3.70/1.27 % (939422)------------------------------
% 3.70/1.27 % (939422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.27 % (939422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.27 % (939422)CaDiCaL version: 2.1.3
% 3.70/1.27 % (939422)Termination reason: Instruction limit
% 3.70/1.27 % (939422)Termination phase: Saturation
% 3.70/1.27 % (939422)Time elapsed: 0.073 s
% 3.70/1.27 % (939422)Peak memory usage: 89 MB
% 3.70/1.27 % (939422)Instructions burned: 118 (million)
% 3.70/1.27 % (939421)Instruction limit reached!
% 3.70/1.27 % (939421)------------------------------
% 3.70/1.27 % (939421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.27 % (939421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.27 % (939421)CaDiCaL version: 2.1.3
% 3.70/1.27 % (939421)Termination reason: Instruction limit
% 3.70/1.27 % (939421)Termination phase: Saturation
% 3.70/1.27 % (939421)Time elapsed: 0.106 s
% 3.70/1.27 % (939421)Peak memory usage: 89 MB
% 3.70/1.27 % (939421)Instructions burned: 181 (million)
% 3.70/1.27 % (939430)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=3868014361:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.70/1.27 % (939430)Instruction limit reached!
% 3.70/1.27 % (939430)------------------------------
% 3.70/1.27 % (939430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.27 % (939430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.27 % (939430)CaDiCaL version: 2.1.3
% 3.70/1.27 % (939430)Termination reason: Instruction limit
% 3.70/1.27 % (939430)Termination phase: Saturation
% 3.70/1.27 % (939430)Time elapsed: 0.047 s
% 3.70/1.27 % (939430)Peak memory usage: 89 MB
% 3.70/1.27 % (939430)Instructions burned: 146 (million)
% 3.70/1.27 % (939431)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1821213165: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)
% 3.70/1.27 % (939431)Also succeeded, but the first one will report.
% 3.70/1.27 % (939433)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1041463262:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.70/1.27 % (939434)lrs+10_64_to=lpo:sil=8000:random_seed=856798140:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 3.70/1.27 % (939434)Instruction limit reached!
% 3.70/1.27 % (939434)------------------------------
% 3.70/1.27 % (939434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.27 % (939434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.27 % (939434)CaDiCaL version: 2.1.3
% 3.70/1.27 % (939434)Termination reason: Instruction limit
% 3.70/1.27 % (939434)Termination phase: Saturation
% 3.70/1.27 % (939434)Time elapsed: 0.040 s
% 3.70/1.27 % (939434)Peak memory usage: 89 MB
% 3.70/1.27 % (939434)Instructions burned: 129 (million)
% 3.70/1.27 % (939419)Refutation found. Thanks to Tanya!
% 3.70/1.27 % SZS status Unsatisfiable for theBenchmark
% 3.70/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/1.28 % (939419)------------------------------
% 3.70/1.28 % (939419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (939419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (939419)CaDiCaL version: 2.1.3
% 3.70/1.28 % (939419)Termination reason: Refutation
% 3.70/1.28 % (939419)Time elapsed: 0.032 s
% 3.70/1.28 % (939419)Peak memory usage: 89 MB
% 3.70/1.28 % (939419)Instructions burned: 48 (million)
% 3.70/1.28 % (939419)------------------------------
% 3.70/1.28 % (939419)------------------------------
% 3.70/1.28 % (939411)Success in time 0.44 s
% 3.70/1.28 % Vampire exiting
%------------------------------------------------------------------------------