%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD009-3 : 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 : n011.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 09:48:58 AM UTC 2026
% Result : Unsatisfiable 0.29s 1.91s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 31 ~; 23 |; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 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/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( product(X0,X1,X2)
| ~ product(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f18,axiom,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
fof(f20,axiom,
! [X0,X1] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_multiplication) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,negated_conjecture,
! [X0] : ~ product(a,X0,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_4) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ product(a,X0,X1)
| ~ product(X0,X2,X3)
| ~ product(X1,X2,b) ),
inference(resolution,[],[f6,f30]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X1,b)
| ~ product(X0,X1,X2)
| ~ product(X0,a,X3) ),
inference(resolution,[],[f77,f10]) ).
fof(f459,plain,
! [X0,X1] :
( ~ product(X0,b,X1)
| ~ product(X0,a,multiplicative_identity)
| ~ defined(b) ),
inference(resolution,[],[f163,f8]) ).
fof(f466,plain,
! [X0,X1] :
( ~ product(X0,a,multiplicative_identity)
| ~ product(X0,b,X1) ),
inference(forward_subsumption_resolution,[],[f459,f28]) ).
fof(f980,plain,
! [X0] :
( ~ product(multiplicative_inverse(a),b,X0)
| sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(resolution,[],[f466,f9]) ).
fof(f981,plain,
! [X0] :
( ~ product(multiplicative_inverse(a),b,X0)
| ~ defined(a) ),
inference(forward_subsumption_resolution,[],[f980,f29]) ).
fof(f982,plain,
! [X0] : ~ product(multiplicative_inverse(a),b,X0),
inference(forward_subsumption_resolution,[],[f981,f27]) ).
fof(f994,plain,
( ~ defined(multiplicative_inverse(a))
| ~ defined(b) ),
inference(resolution,[],[f982,f20]) ).
fof(f995,plain,
~ defined(multiplicative_inverse(a)),
inference(forward_subsumption_resolution,[],[f994,f28]) ).
fof(f1006,plain,
( ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[],[f995,f18]) ).
fof(f1007,plain,
sum(additive_identity,a,additive_identity),
inference(forward_subsumption_resolution,[],[f1006,f27]) ).
fof(f1008,plain,
$false,
inference(forward_subsumption_resolution,[],[f1007,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n011.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 00:22:31 UTC 2026
% 0.26/0.28 % CPUTime :
% 0.26/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.33 Running first-order theorem proving
% 0.26/0.33 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
% 0.29/1.91 % (3946193)Input is clausal, will run a generic CNF schedule.
% 0.29/1.91 % (3946200)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=1428198451:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.29/1.91 % (3946206)dis-21_1_sil=8000:lcm=predicate:random_seed=1890408665: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)
% 0.29/1.91 % (3946202)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1878239580:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.29/1.91 % (3946205)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=337912025:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.29/1.91 % (3946201)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=225123806:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.29/1.91 % (3946204)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1505123579:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.29/1.91 % (3946203)lrs+10_1_sil=8000:sp=occurrence:random_seed=3097918698:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.29/1.91 % (3946203)Refutation not found, incomplete strategy
% 0.29/1.91 % (3946203)------------------------------
% 0.29/1.91 % (3946203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.91 % (3946203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.91 % (3946203)CaDiCaL version: 2.1.3
% 0.29/1.91 % (3946203)Termination reason: Refutation not found, incomplete strategy
% 0.29/1.91 % (3946203)Time elapsed: 0.002 s
% 0.29/1.91 % (3946203)Peak memory usage: 87 MB
% 0.29/1.91 % (3946203)Instructions burned: 1 (million)
% 0.29/1.91 % (3946205)First to succeed.
% 0.29/1.91 % (3946205)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3946193"
% 0.29/1.91 % (3946204)Instruction limit reached!
% 0.29/1.91 % (3946204)------------------------------
% 0.29/1.91 % (3946204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.91 % (3946204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.91 % (3946204)CaDiCaL version: 2.1.3
% 0.29/1.91 % (3946204)Termination reason: Instruction limit
% 0.29/1.91 % (3946204)Termination phase: Saturation
% 0.29/1.91 % (3946204)Time elapsed: 0.100 s
% 0.29/1.91 % (3946204)Peak memory usage: 88 MB
% 0.29/1.91 % (3946204)Instructions burned: 114 (million)
% 0.29/1.91 % (3946206)Instruction limit reached!
% 0.29/1.91 % (3946206)------------------------------
% 0.29/1.91 % (3946206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.91 % (3946206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.91 % (3946206)CaDiCaL version: 2.1.3
% 0.29/1.91 % (3946206)Termination reason: Instruction limit
% 0.29/1.91 % (3946206)Termination phase: Saturation
% 0.29/1.91 % (3946206)Time elapsed: 0.121 s
% 0.29/1.91 % (3946206)Peak memory usage: 89 MB
% 0.29/1.91 % (3946206)Instructions burned: 117 (million)
% 0.29/1.91 % (3946200)Also succeeded, but the first one will report.
% 0.29/1.91 % (3946203)------------------------------
% 0.29/1.91 % (3946203)------------------------------
% 0.29/1.91 % (3946215)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2139899215: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)
% 0.29/1.91 % (3946214)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=1672440063:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 0.29/1.91 % (3946205)Refutation found. Thanks to Tanya!
% 0.29/1.91 % SZS status Unsatisfiable for theBenchmark
% 0.29/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/1.91 % (3946205)------------------------------
% 0.29/1.91 % (3946205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.91 % (3946205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.91 % (3946205)CaDiCaL version: 2.1.3
% 0.29/1.91 % (3946205)Termination reason: Refutation
% 0.29/1.91 % (3946205)Time elapsed: 0.048 s
% 0.29/1.91 % (3946205)Peak memory usage: 88 MB
% 0.29/1.91 % (3946205)Instructions burned: 44 (million)
% 0.29/1.91 % (3946205)------------------------------
% 0.29/1.91 % (3946205)------------------------------
% 0.29/1.91 % (3946193)Success in time 0.718 s
% 0.29/1.91 % Vampire exiting
%------------------------------------------------------------------------------