%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 11:52:20 AM UTC 2026
% Result : Theorem 2.63s 1.34s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 64 ( 28 ~; 16 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 61 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ( ! [X0,X1] :
( ~ a_truth(implies(X0,X1))
| ~ a_truth(X0)
| a_truth(X1) )
& ! [X0,X1] : a_truth(implies(X0,implies(X1,X0)))
& ! [X0,X1,X2] : a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2))))
& ! [X0,X1] : a_truth(implies(implies(not(X0),not(X1)),implies(X1,X0)))
& ? [X3] : ~ a_truth(implies(X3,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm147) ).
fof(f2,negated_conjecture,
~ ~ ( ! [X0,X1] :
( ~ a_truth(implies(X0,X1))
| ~ a_truth(X0)
| a_truth(X1) )
& ! [X0,X1] : a_truth(implies(X0,implies(X1,X0)))
& ! [X0,X1,X2] : a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2))))
& ! [X0,X1] : a_truth(implies(implies(not(X0),not(X1)),implies(X1,X0)))
& ? [X3] : ~ a_truth(implies(X3,X3)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ( ! [X0,X1] :
( ~ a_truth(implies(X0,X1))
| ~ a_truth(X0)
| a_truth(X1) )
& ! [X2,X3] : a_truth(implies(X2,implies(X3,X2)))
& ! [X4,X5,X6] : a_truth(implies(implies(X4,implies(X5,X6)),implies(implies(X4,X5),implies(X4,X6))))
& ! [X7,X8] : a_truth(implies(implies(not(X7),not(X8)),implies(X8,X7)))
& ? [X9] : ~ a_truth(implies(X9,X9)) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0,X1] :
( ~ a_truth(implies(X0,X1))
| ~ a_truth(X0)
| a_truth(X1) )
& ! [X2,X3] : a_truth(implies(X2,implies(X3,X2)))
& ! [X4,X5,X6] : a_truth(implies(implies(X4,implies(X5,X6)),implies(implies(X4,X5),implies(X4,X6))))
& ! [X7,X8] : a_truth(implies(implies(not(X7),not(X8)),implies(X8,X7)))
& ? [X9] : ~ a_truth(implies(X9,X9)) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( ! [X0,X1] :
( ~ a_truth(implies(X0,X1))
| ~ a_truth(X0)
| a_truth(X1) )
& ! [X2,X3] : a_truth(implies(X2,implies(X3,X2)))
& ! [X4,X5,X6] : a_truth(implies(implies(X4,implies(X5,X6)),implies(implies(X4,X5),implies(X4,X6))))
& ! [X7,X8] : a_truth(implies(implies(not(X7),not(X8)),implies(X8,X7)))
& ~ a_truth(implies(sK0,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X9,sK0)],[f4]) ).
fof(f6,plain,
~ a_truth(implies(sK0,sK0)),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
! [X6,X4,X5] : a_truth(implies(implies(X4,implies(X5,X6)),implies(implies(X4,X5),implies(X4,X6)))),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X2,X3] : a_truth(implies(X2,implies(X3,X2))),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( ~ a_truth(implies(X0,X1))
| ~ a_truth(X0)
| a_truth(X1) ),
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
! [X2,X0,X1] :
( a_truth(implies(implies(X0,X1),implies(X0,X2)))
| ~ a_truth(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f8,f10]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ~ a_truth(implies(X0,implies(X1,X2)))
| ~ a_truth(implies(X0,X1))
| a_truth(implies(X0,X2)) ),
inference(resolution,[],[f15,f10]) ).
fof(f21,plain,
! [X0,X1] :
( a_truth(implies(X0,X0))
| ~ a_truth(implies(X0,X1)) ),
inference(resolution,[],[f17,f9]) ).
fof(f31,plain,
! [X0] : ~ a_truth(implies(sK0,X0)),
inference(resolution,[],[f21,f6]) ).
fof(f39,plain,
$false,
inference(resolution,[],[f31,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:43:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.63/1.34 % (3696409)Detected formulas, will run a generic FOF schedule.
% 2.63/1.34 % (3696548)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3653977518:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.34 % (3696548)First to succeed.
% 2.63/1.34 % (3696548)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3696409"
% 2.63/1.34 % (3696550)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=119289151:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.34 % (3696545)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2838526197:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.34 % (3696552)dis-21_1_sil=8000:lcm=predicate:random_seed=3918856065:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.63/1.34 % (3696541)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=2336249705:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.34 % (3696543)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=52017077:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.34 % (3696546)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3313402334:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.34 % (3696550)Also succeeded, but the first one will report.
% 2.63/1.34 % (3696552)Also succeeded, but the first one will report.
% 2.63/1.34 % (3696546)Also succeeded, but the first one will report.
% 2.63/1.34 % (3696548)Refutation found. Thanks to Tanya!
% 2.63/1.34 % SZS status Theorem for theBenchmark
% 2.63/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.34 % (3696548)------------------------------
% 2.63/1.34 % (3696548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.34 % (3696548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.34 % (3696548)CaDiCaL version: 2.1.3
% 2.63/1.34 % (3696548)Termination reason: Refutation
% 2.63/1.34 % (3696548)Time elapsed: 0.001 s
% 2.63/1.34 % (3696548)Peak memory usage: 88 MB
% 2.63/1.34 % (3696548)Instructions burned: 1 (million)
% 2.63/1.34 % (3696548)------------------------------
% 2.63/1.34 % (3696548)------------------------------
% 2.63/1.34 % (3696409)Success in time 0.307 s
% 2.63/1.34 % Vampire exiting
%------------------------------------------------------------------------------