%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD009-1 : 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 : n019.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 5.10s 1.48s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 49 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X0,X1] :
( equalish(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X2))
| ~ defined(X0)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication) ).
fof(f6,axiom,
! [X0] :
( equalish(multiply(multiplicative_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f15,axiom,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
fof(f31,negated_conjecture,
! [X0] : ~ equalish(multiply(a,X0),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_not_equal_to_b_4) ).
fof(f35,plain,
! [X0,X1] :
( ~ equalish(multiply(a,X0),X1)
| ~ equalish(X1,b) ),
inference(resolution,[],[f31,f23]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ equalish(multiply(a,X1),X2)
| ~ equalish(X0,b)
| ~ equalish(X2,X0) ),
inference(resolution,[],[f35,f23]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ equalish(X0,b)
| ~ equalish(multiply(multiply(a,X1),X2),X0)
| ~ defined(a)
| ~ defined(X1)
| ~ defined(X2) ),
inference(resolution,[],[f49,f5]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ equalish(multiply(multiply(a,X1),X2),X0)
| ~ equalish(X0,b)
| ~ defined(X1)
| ~ defined(X2) ),
inference(forward_subsumption_resolution,[],[f109,f28]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ equalish(multiply(X0,X1),b)
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X1)
| ~ equalish(multiply(a,X2),X0) ),
inference(resolution,[],[f116,f25]) ).
fof(f301,plain,
! [X2,X0,X1] :
( ~ equalish(multiply(a,X2),X0)
| ~ defined(X2)
| ~ defined(X1)
| ~ equalish(multiply(X0,X1),b) ),
inference(duplicate_literal_removal,[],[f293]) ).
fof(f794,plain,
! [X0] :
( ~ defined(multiplicative_inverse(a))
| ~ defined(X0)
| ~ equalish(multiply(multiplicative_identity,X0),b)
| ~ defined(a)
| equalish(a,additive_identity) ),
inference(resolution,[],[f301,f7]) ).
fof(f800,plain,
! [X0] :
( ~ defined(X0)
| ~ equalish(multiply(multiplicative_identity,X0),b)
| ~ defined(a)
| equalish(a,additive_identity) ),
inference(forward_subsumption_resolution,[],[f794,f15]) ).
fof(f803,plain,
! [X0] :
( ~ defined(X0)
| ~ equalish(multiply(multiplicative_identity,X0),b)
| equalish(a,additive_identity) ),
inference(forward_subsumption_resolution,[],[f800,f28]) ).
fof(f805,plain,
! [X0] :
( ~ equalish(multiply(multiplicative_identity,X0),b)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[],[f803,f30]) ).
fof(f806,plain,
( ~ defined(b)
| ~ defined(b) ),
inference(resolution,[],[f805,f6]) ).
fof(f809,plain,
~ defined(b),
inference(duplicate_literal_removal,[],[f806]) ).
fof(f810,plain,
$false,
inference(forward_subsumption_resolution,[],[f809,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD009-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:22:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 5.10/1.48 % (420858)Input is clausal, will run a generic CNF schedule.
% 5.10/1.48 % (420863)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=125654289:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.10/1.48 % (420868)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2224523796:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.10/1.48 % (420864)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2089867179:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.10/1.48 % (420866)lrs+10_1_sil=8000:sp=occurrence:random_seed=4062274602:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.10/1.48 % (420867)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4087400656:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.10/1.48 % (420865)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1324776271:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.10/1.48 % (420869)dis-21_1_sil=8000:lcm=predicate:random_seed=1077324927: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)
% 5.10/1.48 % (420866)Instruction limit reached!
% 5.10/1.48 % (420866)------------------------------
% 5.10/1.48 % (420866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.48 % (420866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.48 % (420866)CaDiCaL version: 2.1.3
% 5.10/1.48 % (420866)Termination reason: Instruction limit
% 5.10/1.48 % (420866)Termination phase: Saturation
% 5.10/1.48 % (420866)Time elapsed: 0.067 s
% 5.10/1.48 % (420866)Peak memory usage: 89 MB
% 5.10/1.48 % (420866)Instructions burned: 108 (million)
% 5.10/1.48 % (420867)Instruction limit reached!
% 5.10/1.48 % (420867)------------------------------
% 5.10/1.48 % (420867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.48 % (420867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.48 % (420867)CaDiCaL version: 2.1.3
% 5.10/1.48 % (420867)Termination reason: Instruction limit
% 5.10/1.48 % (420867)Termination phase: Saturation
% 5.10/1.48 % (420867)Time elapsed: 0.070 s
% 5.10/1.48 % (420867)Peak memory usage: 88 MB
% 5.10/1.48 % (420867)Instructions burned: 115 (million)
% 5.10/1.48 % (420869)Instruction limit reached!
% 5.10/1.48 % (420869)------------------------------
% 5.10/1.48 % (420869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.48 % (420869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.48 % (420869)CaDiCaL version: 2.1.3
% 5.10/1.48 % (420869)Termination reason: Instruction limit
% 5.10/1.48 % (420869)Termination phase: Saturation
% 5.10/1.48 % (420869)Time elapsed: 0.073 s
% 5.10/1.48 % (420869)Peak memory usage: 89 MB
% 5.10/1.48 % (420869)Instructions burned: 118 (million)
% 5.10/1.48 % (420868)Instruction limit reached!
% 5.10/1.48 % (420868)------------------------------
% 5.10/1.48 % (420868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.48 % (420868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.48 % (420868)CaDiCaL version: 2.1.3
% 5.10/1.48 % (420868)Termination reason: Instruction limit
% 5.10/1.48 % (420868)Termination phase: Saturation
% 5.10/1.48 % (420868)Time elapsed: 0.118 s
% 5.10/1.48 % (420868)Peak memory usage: 89 MB
% 5.10/1.48 % (420868)Instructions burned: 180 (million)
% 5.10/1.48 % (420877)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=2839642085:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.10/1.48 % (420878)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3445432068: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)
% 5.10/1.48 % (420877)Refutation not found, incomplete strategy
% 5.10/1.48 % (420877)------------------------------
% 5.10/1.48 % (420877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.48 % (420877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.48 % (420877)CaDiCaL version: 2.1.3
% 5.10/1.48 % (420877)Termination reason: Refutation not found, incomplete strategy
% 5.10/1.48 % (420877)Time elapsed: 0.001 s
% 5.10/1.48 % (420877)Peak memory usage: 87 MB
% 5.10/1.48 % (420879)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3964009864:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.10/1.48 % (420879)First to succeed.
% 5.10/1.48 % (420879)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-420858"
% 5.10/1.48 % (420880)lrs+10_64_to=lpo:sil=8000:random_seed=1349049063:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.10/1.48 % (420878)Instruction limit reached!
% 5.10/1.48 % (420878)------------------------------
% 5.10/1.48 % (420878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.48 % (420878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.48 % (420878)CaDiCaL version: 2.1.3
% 5.10/1.48 % (420878)Termination reason: Instruction limit
% 5.10/1.48 % (420878)Termination phase: Saturation
% 5.10/1.48 % (420878)Time elapsed: 0.096 s
% 5.10/1.48 % (420878)Peak memory usage: 94 MB
% 5.10/1.48 % (420878)Instructions burned: 191 (million)
% 5.10/1.48 % (420880)Instruction limit reached!
% 5.10/1.48 % (420880)------------------------------
% 5.10/1.48 % (420880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.48 % (420880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.48 % (420880)CaDiCaL version: 2.1.3
% 5.10/1.48 % (420880)Termination reason: Instruction limit
% 5.10/1.48 % (420880)Termination phase: Saturation
% 5.10/1.48 % (420880)Time elapsed: 0.082 s
% 5.10/1.48 % (420880)Peak memory usage: 89 MB
% 5.10/1.48 % (420880)Instructions burned: 128 (million)
% 5.10/1.48 % (420863)Also succeeded, but the first one will report.
% 5.10/1.48 % (420885)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3522542673:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.10/1.48 % (420877)------------------------------
% 5.10/1.48 % (420877)------------------------------
% 5.10/1.48 % (420886)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3806746293:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.10/1.48 % (420879)Refutation found. Thanks to Tanya!
% 5.10/1.48 % SZS status Unsatisfiable for theBenchmark
% 5.10/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 5.10/1.48 % (420879)------------------------------
% 5.10/1.48 % (420879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.48 % (420879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.48 % (420879)CaDiCaL version: 2.1.3
% 5.10/1.48 % (420879)Termination reason: Refutation
% 5.10/1.48 % (420879)Time elapsed: 0.017 s
% 5.10/1.48 % (420879)Peak memory usage: 88 MB
% 5.10/1.48 % (420879)Instructions burned: 22 (million)
% 5.10/1.48 % (420879)------------------------------
% 5.10/1.48 % (420879)------------------------------
% 5.10/1.48 % (420858)Success in time 0.639 s
% 5.10/1.48 % Vampire exiting
%------------------------------------------------------------------------------