%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD031-5 : 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 09:49:06 AM UTC 2026
% Result : Unsatisfiable 3.49s 1.19s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 43 ( 24 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X4,X5,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(X0,X1,X2)
| ~ product(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
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,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_2) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
fof(f35,plain,
( ~ defined(a)
| defined(multiplicative_inverse(a)) ),
inference(resolution,[],[f18,f29]) ).
fof(f36,plain,
defined(multiplicative_inverse(a)),
inference(forward_subsumption_resolution,[],[f35,f27]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,multiplicative_inverse(a))
| ~ product(X0,X2,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X1) ),
inference(resolution,[],[f6,f30]) ).
fof(f95,plain,
! [X0] :
( ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[],[f56,f8]) ).
fof(f100,plain,
! [X0] :
( ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(forward_subsumption_resolution,[],[f95,f36]) ).
fof(f113,plain,
! [X0] :
( ~ product(multiplicative_inverse(a),X0,multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(resolution,[],[f100,f10]) ).
fof(f173,plain,
( ~ product(multiplicative_identity,a,multiplicative_identity)
| sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(resolution,[],[f113,f9]) ).
fof(f178,plain,
( sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(forward_subsumption_resolution,[],[f173,f28]) ).
fof(f179,plain,
~ defined(a),
inference(forward_subsumption_resolution,[],[f178,f29]) ).
fof(f180,plain,
$false,
inference(forward_subsumption_resolution,[],[f179,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n002.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 00:33:08 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 3.49/1.19 % (940755)Input is clausal, will run a generic CNF schedule.
% 3.49/1.19 % (940766)dis-21_1_sil=8000:lcm=predicate:random_seed=968234871: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)
% 3.49/1.19 % (940760)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=4198655688:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.49/1.19 % (940765)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3015649094:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.49/1.19 % (940763)lrs+10_1_sil=8000:sp=occurrence:random_seed=2214409200:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.49/1.19 % (940761)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3884453538:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.49/1.19 % (940762)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3115334249:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.49/1.19 % (940764)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=309097757:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.49/1.19 % (940764)First to succeed.
% 3.49/1.19 % (940764)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-940755"
% 3.49/1.19 % (940766)Instruction limit reached!
% 3.49/1.19 % (940766)------------------------------
% 3.49/1.19 % (940766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.19 % (940766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.19 % (940766)CaDiCaL version: 2.1.3
% 3.49/1.19 % (940766)Termination reason: Instruction limit
% 3.49/1.19 % (940766)Termination phase: Saturation
% 3.49/1.19 % (940766)Time elapsed: 0.039 s
% 3.49/1.19 % (940766)Peak memory usage: 89 MB
% 3.49/1.19 % (940766)Instructions burned: 119 (million)
% 3.49/1.19 % (940763)Also succeeded, but the first one will report.
% 3.49/1.19 % (940765)Also succeeded, but the first one will report.
% 3.49/1.19 % (940774)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=1486388788:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.49/1.19 % (940774)Instruction limit reached!
% 3.49/1.19 % (940774)------------------------------
% 3.49/1.19 % (940774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.19 % (940774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.19 % (940774)CaDiCaL version: 2.1.3
% 3.49/1.19 % (940774)Termination reason: Instruction limit
% 3.49/1.19 % (940774)Termination phase: Saturation
% 3.49/1.19 % (940774)Time elapsed: 0.037 s
% 3.49/1.19 % (940774)Peak memory usage: 88 MB
% 3.49/1.19 % (940774)Instructions burned: 145 (million)
% 3.49/1.19 % (940776)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1021149627:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 3.49/1.19 % (940776)Also succeeded, but the first one will report.
% 3.49/1.19 % (940764)Refutation found. Thanks to Tanya!
% 3.49/1.19 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.19 % (940764)------------------------------
% 3.49/1.19 % (940764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.19 % (940764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.19 % (940764)CaDiCaL version: 2.1.3
% 3.49/1.19 % (940764)Termination reason: Refutation
% 3.49/1.19 % (940764)Time elapsed: 0.005 s
% 3.49/1.19 % (940764)Peak memory usage: 88 MB
% 3.49/1.19 % (940764)Instructions burned: 6 (million)
% 3.49/1.19 % (940764)------------------------------
% 3.49/1.19 % (940764)------------------------------
% 3.49/1.19 % (940755)Success in time 0.421 s
% 3.49/1.19 % Vampire exiting
%------------------------------------------------------------------------------