%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD049-4 : 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 : n016.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 09:49:12 AM UTC 2026
% Result : Unsatisfiable 3.92s 1.32s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 63 ( 31 ~; 32 |; 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 : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 32 ( 32 !; 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(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2)
| ~ product(X3,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication_2) ).
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(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,axiom,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
fof(f30,axiom,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
fof(f33,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).
fof(f34,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_8) ).
fof(f35,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_9) ).
fof(f36,negated_conjecture,
product(c,multiplicative_inverse(d),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_10) ).
fof(f37,negated_conjecture,
product(a,d,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_11) ).
fof(f38,negated_conjecture,
~ product(b,c,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_12) ).
fof(f44,plain,
! [X0] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(resolution,[],[f10,f8]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ product(X1,d,X2)
| ~ product(X0,X1,a)
| product(X0,X2,k) ),
inference(resolution,[],[f6,f37]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,multiplicative_inverse(X1),X2)
| product(X2,X1,X3)
| ~ product(X0,multiplicative_identity,X3)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(resolution,[],[f7,f9]) ).
fof(f472,plain,
! [X0] :
( product(s,b,X0)
| ~ product(a,multiplicative_identity,X0)
| sum(additive_identity,b,additive_identity)
| ~ defined(b) ),
inference(resolution,[],[f75,f35]) ).
fof(f473,plain,
! [X0] :
( product(s,d,X0)
| ~ product(c,multiplicative_identity,X0)
| sum(additive_identity,d,additive_identity)
| ~ defined(d) ),
inference(resolution,[],[f75,f36]) ).
fof(f475,plain,
! [X0] :
( product(s,d,X0)
| ~ product(c,multiplicative_identity,X0)
| ~ defined(d) ),
inference(forward_subsumption_resolution,[],[f473,f34]) ).
fof(f476,plain,
! [X0] :
( product(s,b,X0)
| ~ product(a,multiplicative_identity,X0)
| ~ defined(b) ),
inference(forward_subsumption_resolution,[],[f472,f33]) ).
fof(f479,plain,
! [X0] :
( ~ product(c,multiplicative_identity,X0)
| product(s,d,X0) ),
inference(forward_subsumption_resolution,[],[f475,f30]) ).
fof(f480,plain,
! [X0] :
( ~ product(a,multiplicative_identity,X0)
| product(s,b,X0) ),
inference(forward_subsumption_resolution,[],[f476,f28]) ).
fof(f551,plain,
( product(s,d,c)
| ~ defined(c) ),
inference(resolution,[],[f479,f44]) ).
fof(f552,plain,
product(s,d,c),
inference(forward_subsumption_resolution,[],[f551,f29]) ).
fof(f556,plain,
! [X0] :
( ~ product(X0,s,a)
| product(X0,c,k) ),
inference(resolution,[],[f552,f64]) ).
fof(f568,plain,
( product(s,b,a)
| ~ defined(a) ),
inference(resolution,[],[f480,f44]) ).
fof(f569,plain,
product(s,b,a),
inference(forward_subsumption_resolution,[],[f568,f27]) ).
fof(f573,plain,
product(b,s,a),
inference(resolution,[],[f569,f10]) ).
fof(f3021,plain,
product(b,c,k),
inference(resolution,[],[f556,f573]) ).
fof(f3022,plain,
$false,
inference(forward_subsumption_resolution,[],[f3021,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD049-4 : 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 : n016.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 00:44:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.92/1.32 % (14615)Input is clausal, will run a generic CNF schedule.
% 3.92/1.32 % (14620)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=2394473235:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.92/1.32 % (14625)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1551921708:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.92/1.32 % (14623)lrs+10_1_sil=8000:sp=occurrence:random_seed=253141347:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.92/1.32 % (14624)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1066369006:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.92/1.32 % (14621)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=259469080:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.92/1.32 % (14622)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2606265004:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.92/1.32 % (14626)dis-21_1_sil=8000:lcm=predicate:random_seed=1920617369: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)
% 3.92/1.32 % (14623)First to succeed.
% 3.92/1.32 % (14623)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14615"
% 3.92/1.32 % (14624)Instruction limit reached!
% 3.92/1.32 % (14624)------------------------------
% 3.92/1.32 % (14624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.32 % (14624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.32 % (14624)CaDiCaL version: 2.1.3
% 3.92/1.32 % (14624)Termination reason: Instruction limit
% 3.92/1.32 % (14624)Termination phase: Saturation
% 3.92/1.32 % (14624)Time elapsed: 0.066 s
% 3.92/1.32 % (14624)Peak memory usage: 88 MB
% 3.92/1.32 % (14624)Instructions burned: 114 (million)
% 3.92/1.32 % (14626)Instruction limit reached!
% 3.92/1.32 % (14626)------------------------------
% 3.92/1.32 % (14626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.32 % (14626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.32 % (14626)CaDiCaL version: 2.1.3
% 3.92/1.32 % (14626)Termination reason: Instruction limit
% 3.92/1.32 % (14626)Termination phase: Saturation
% 3.92/1.32 % (14626)Time elapsed: 0.074 s
% 3.92/1.32 % (14626)Peak memory usage: 89 MB
% 3.92/1.32 % (14626)Instructions burned: 117 (million)
% 3.92/1.32 % (14625)Instruction limit reached!
% 3.92/1.32 % (14625)------------------------------
% 3.92/1.32 % (14625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.32 % (14625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.32 % (14625)CaDiCaL version: 2.1.3
% 3.92/1.32 % (14625)Termination reason: Instruction limit
% 3.92/1.32 % (14625)Termination phase: Saturation
% 3.92/1.32 % (14625)Time elapsed: 0.106 s
% 3.92/1.32 % (14625)Peak memory usage: 88 MB
% 3.92/1.32 % (14625)Instructions burned: 180 (million)
% 3.92/1.32 % (14634)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=2375670140:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.92/1.32 % (14635)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=398797182: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)
% 3.92/1.32 % (14635)Also succeeded, but the first one will report.
% 3.92/1.32 % (14636)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3853800199:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.92/1.32 % (14634)Instruction limit reached!
% 3.92/1.32 % (14634)------------------------------
% 3.92/1.32 % (14634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.32 % (14634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.32 % (14634)CaDiCaL version: 2.1.3
% 3.92/1.32 % (14634)Termination reason: Instruction limit
% 3.92/1.32 % (14634)Termination phase: Saturation
% 3.92/1.32 % (14634)Time elapsed: 0.083 s
% 3.92/1.32 % (14634)Peak memory usage: 89 MB
% 3.92/1.32 % (14634)Instructions burned: 143 (million)
% 3.92/1.32 % (14623)Refutation found. Thanks to Tanya!
% 3.92/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.92/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.32 % (14623)------------------------------
% 3.92/1.32 % (14623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.32 % (14623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.32 % (14623)CaDiCaL version: 2.1.3
% 3.92/1.32 % (14623)Termination reason: Refutation
% 3.92/1.32 % (14623)Time elapsed: 0.057 s
% 3.92/1.32 % (14623)Peak memory usage: 89 MB
% 3.92/1.32 % (14623)Instructions burned: 91 (million)
% 3.92/1.32 % (14623)------------------------------
% 3.92/1.32 % (14623)------------------------------
% 3.92/1.32 % (14615)Success in time 0.46 s
% 3.92/1.32 % Vampire exiting
%------------------------------------------------------------------------------