%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD013-1 : 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 : n013.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 09:49:00 AM UTC 2026
% Result : Unsatisfiable 2.88s 1.17s
% Output : Refutation 2.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 34 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( equalish(add(X0,X1),add(X1,X0))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f24,axiom,
! [X2,X0,X1] :
( equalish(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ equalish(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
fof(f29,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f32,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b_5) ).
fof(f33,negated_conjecture,
equalish(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_equals_d_6) ).
fof(f34,negated_conjecture,
~ equalish(add(a,c),add(d,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_not_equal_to_add_7) ).
fof(f40,plain,
! [X0] :
( ~ equalish(add(a,c),X0)
| ~ equalish(X0,add(d,b)) ),
inference(resolution,[],[f23,f34]) ).
fof(f84,plain,
! [X0] :
( ~ defined(c)
| ~ equalish(a,X0)
| ~ equalish(add(X0,c),add(d,b)) ),
inference(resolution,[],[f24,f40]) ).
fof(f89,plain,
! [X0] :
( ~ equalish(add(X0,c),add(d,b))
| ~ equalish(a,X0) ),
inference(forward_subsumption_resolution,[],[f84,f30]) ).
fof(f98,plain,
! [X0,X1] :
( ~ equalish(add(X0,c),X1)
| ~ equalish(a,X0)
| ~ equalish(X1,add(d,b)) ),
inference(resolution,[],[f89,f23]) ).
fof(f416,plain,
! [X0] :
( ~ equalish(a,X0)
| ~ equalish(add(c,X0),add(d,b))
| ~ defined(X0)
| ~ defined(c) ),
inference(resolution,[],[f98,f4]) ).
fof(f433,plain,
! [X0] :
( ~ equalish(add(c,X0),add(d,b))
| ~ equalish(a,X0)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[],[f416,f30]) ).
fof(f2520,plain,
( ~ equalish(a,b)
| ~ defined(b)
| ~ defined(b)
| ~ equalish(c,d) ),
inference(resolution,[],[f433,f24]) ).
fof(f2524,plain,
( ~ equalish(a,b)
| ~ defined(b)
| ~ equalish(c,d) ),
inference(duplicate_literal_removal,[],[f2520]) ).
fof(f2531,plain,
( ~ defined(b)
| ~ equalish(c,d) ),
inference(forward_subsumption_resolution,[],[f2524,f32]) ).
fof(f2537,plain,
~ equalish(c,d),
inference(forward_subsumption_resolution,[],[f2531,f29]) ).
fof(f2543,plain,
$false,
inference(forward_subsumption_resolution,[],[f2537,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 00:24:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 2.88/1.17 % (1741229)Input is clausal, will run a generic CNF schedule.
% 2.88/1.17 % (1741238)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4265575485:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.88/1.17 % (1741238)First to succeed.
% 2.88/1.17 % (1741238)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1741229"
% 2.88/1.17 % (1741234)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=3200616530:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.88/1.17 % (1741235)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3427530746:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.88/1.17 % (1741237)lrs+10_1_sil=8000:sp=occurrence:random_seed=4265195364:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.88/1.17 % (1741236)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3589695736:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.88/1.17 % (1741239)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1855694425:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.88/1.17 % (1741240)dis-21_1_sil=8000:lcm=predicate:random_seed=110064497: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)
% 2.88/1.17 % (1741237)Also succeeded, but the first one will report.
% 2.88/1.17 % (1741239)Also succeeded, but the first one will report.
% 2.88/1.17 % (1741240)Also succeeded, but the first one will report.
% 2.88/1.17 % (1741238)Refutation found. Thanks to Tanya!
% 2.88/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.88/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.88/1.17 % (1741238)------------------------------
% 2.88/1.17 % (1741238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.17 % (1741238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.17 % (1741238)CaDiCaL version: 2.1.3
% 2.88/1.17 % (1741238)Termination reason: Refutation
% 2.88/1.17 % (1741238)Time elapsed: 0.028 s
% 2.88/1.17 % (1741238)Peak memory usage: 89 MB
% 2.88/1.17 % (1741238)Instructions burned: 82 (million)
% 2.88/1.17 % (1741238)------------------------------
% 2.88/1.17 % (1741238)------------------------------
% 2.88/1.17 % (1741229)Success in time 0.318 s
% 2.88/1.17 % Vampire exiting
%------------------------------------------------------------------------------