%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD035-3 : 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 : 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 09:49:07 AM UTC 2026
% Result : Unsatisfiable 4.41s 1.09s
% Output : Refutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 18 ( 13 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 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 : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 17 ( 17 !; 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(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X1,X2)
| ~ product(X3,X4,X0)
| ~ product(X4,X1,X5)
| ~ product(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
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(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f31,negated_conjecture,
product(a,c,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
fof(f32,negated_conjecture,
product(b,c,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
fof(f33,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
fof(f34,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_8) ).
fof(f35,plain,
product(c,a,u),
inference(unit_resulting_resolution,[],[f10,f31]) ).
fof(f36,plain,
product(c,b,u),
inference(unit_resulting_resolution,[],[f10,f32]) ).
fof(f71,plain,
product(multiplicative_identity,b,b),
inference(unit_resulting_resolution,[],[f8,f28]) ).
fof(f109,plain,
product(multiplicative_inverse(c),c,multiplicative_identity),
inference(unit_resulting_resolution,[],[f9,f33,f29]) ).
fof(f337,plain,
~ product(multiplicative_inverse(c),u,b),
inference(unit_resulting_resolution,[],[f7,f34,f35,f109]) ).
fof(f417,plain,
product(multiplicative_inverse(c),u,b),
inference(unit_resulting_resolution,[],[f6,f36,f109,f71]) ).
fof(f420,plain,
$false,
inference(forward_subsumption_resolution,[],[f417,f337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD035-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 00:35:23 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 4.41/1.09 % (941616)Input is clausal, will run a generic CNF schedule.
% 4.41/1.09 % (941627)dis-21_1_sil=8000:lcm=predicate:random_seed=1182727082: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)
% 4.41/1.09 % (941622)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=761692460:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.41/1.09 % (941621)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=79317920:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.41/1.09 % (941625)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3199892047:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.41/1.09 % (941623)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1285131056:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.41/1.09 % (941624)lrs+10_1_sil=8000:sp=occurrence:random_seed=62167522:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.41/1.09 % (941627)Instruction limit reached!
% 4.41/1.09 % (941627)------------------------------
% 4.41/1.09 % (941627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941627)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941627)Termination reason: Instruction limit
% 4.41/1.09 % (941627)Termination phase: Saturation
% 4.41/1.09 % (941627)Time elapsed: 0.039 s
% 4.41/1.09 % (941627)Peak memory usage: 89 MB
% 4.41/1.09 % (941627)Instructions burned: 117 (million)
% 4.41/1.09 % (941626)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1602681286:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.41/1.09 % (941625)Instruction limit reached!
% 4.41/1.09 % (941625)------------------------------
% 4.41/1.09 % (941625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941625)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941625)Termination reason: Instruction limit
% 4.41/1.09 % (941625)Termination phase: Saturation
% 4.41/1.09 % (941625)Time elapsed: 0.063 s
% 4.41/1.09 % (941625)Peak memory usage: 88 MB
% 4.41/1.09 % (941625)Instructions burned: 116 (million)
% 4.41/1.09 % (941624)Instruction limit reached!
% 4.41/1.09 % (941624)------------------------------
% 4.41/1.09 % (941624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941624)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941624)Termination reason: Instruction limit
% 4.41/1.09 % (941624)Termination phase: Saturation
% 4.41/1.09 % (941624)Time elapsed: 0.067 s
% 4.41/1.09 % (941624)Peak memory usage: 88 MB
% 4.41/1.09 % (941624)Instructions burned: 108 (million)
% 4.41/1.09 % (941635)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=4107166631:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.41/1.09 % (941626)Instruction limit reached!
% 4.41/1.09 % (941626)------------------------------
% 4.41/1.09 % (941626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941626)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941626)Termination reason: Instruction limit
% 4.41/1.09 % (941626)Termination phase: Saturation
% 4.41/1.09 % (941626)Time elapsed: 0.114 s
% 4.41/1.09 % (941626)Peak memory usage: 89 MB
% 4.41/1.09 % (941626)Instructions burned: 180 (million)
% 4.41/1.09 % (941635)Instruction limit reached!
% 4.41/1.09 % (941635)------------------------------
% 4.41/1.09 % (941635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941635)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941635)Termination reason: Instruction limit
% 4.41/1.09 % (941635)Termination phase: Saturation
% 4.41/1.09 % (941635)Time elapsed: 0.039 s
% 4.41/1.09 % (941635)Peak memory usage: 89 MB
% 4.41/1.09 % (941635)Instructions burned: 143 (million)
% 4.41/1.09 % (941636)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3400505217:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 4.41/1.09 % (941637)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3619994199:st=4:i=219:sd=3:ss=axioms_2998 on theBenchmark for (2998ds/219Mi)
% 4.41/1.09 % (941636)First to succeed.
% 4.41/1.09 % (941636)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-941616"
% 4.41/1.09 % (941640)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=663744458:avsq=on:i=194:fgj=on:bd=preordered_2997 on theBenchmark for (2997ds/194Mi)
% 4.41/1.09 % (941639)lrs+10_64_to=lpo:sil=8000:random_seed=3894122274:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.41/1.09 % (941640)Instruction limit reached!
% 4.41/1.09 % (941640)------------------------------
% 4.41/1.09 % (941640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941640)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941640)Termination reason: Instruction limit
% 4.41/1.09 % (941640)Termination phase: Saturation
% 4.41/1.09 % (941640)Time elapsed: 0.072 s
% 4.41/1.09 % (941640)Peak memory usage: 89 MB
% 4.41/1.09 % (941640)Instructions burned: 195 (million)
% 4.41/1.09 % (941637)Instruction limit reached!
% 4.41/1.09 % (941637)------------------------------
% 4.41/1.09 % (941637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941637)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941637)Termination reason: Instruction limit
% 4.41/1.09 % (941637)Termination phase: Saturation
% 4.41/1.09 % (941637)Time elapsed: 0.132 s
% 4.41/1.09 % (941637)Peak memory usage: 89 MB
% 4.41/1.09 % (941637)Instructions burned: 220 (million)
% 4.41/1.09 % (941639)Instruction limit reached!
% 4.41/1.09 % (941639)------------------------------
% 4.41/1.09 % (941639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941639)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941639)Termination reason: Instruction limit
% 4.41/1.09 % (941639)Termination phase: Saturation
% 4.41/1.09 % (941639)Time elapsed: 0.079 s
% 4.41/1.09 % (941639)Peak memory usage: 89 MB
% 4.41/1.09 % (941639)Instructions burned: 127 (million)
% 4.41/1.09 % (941645)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3150469626:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 4.41/1.09 % (941645)Instruction limit reached!
% 4.41/1.09 % (941645)------------------------------
% 4.41/1.09 % (941645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941645)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941645)Termination reason: Instruction limit
% 4.41/1.09 % (941645)Termination phase: Saturation
% 4.41/1.09 % (941645)Time elapsed: 0.055 s
% 4.41/1.09 % (941645)Peak memory usage: 90 MB
% 4.41/1.09 % (941645)Instructions burned: 159 (million)
% 4.41/1.09 % (941636)Refutation found. Thanks to Tanya!
% 4.41/1.09 % SZS status Unsatisfiable for theBenchmark
% 4.41/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 4.41/1.09 % (941636)------------------------------
% 4.41/1.09 % (941636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.09 % (941636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.09 % (941636)CaDiCaL version: 2.1.3
% 4.41/1.09 % (941636)Termination reason: Refutation
% 4.41/1.09 % (941636)Time elapsed: 0.008 s
% 4.41/1.09 % (941636)Peak memory usage: 88 MB
% 4.41/1.09 % (941636)Instructions burned: 12 (million)
% 4.41/1.09 % (941636)------------------------------
% 4.41/1.09 % (941636)------------------------------
% 4.41/1.09 % (941616)Success in time 0.58 s
% 4.41/1.09 % Vampire exiting
%------------------------------------------------------------------------------