%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:50:19 PM UTC 2026
% Result : Theorem 2.74s 1.15s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 3 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 95 ( 24 ~; 20 |; 33 &)
% ( 6 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 23 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X3,X0,X4)
=> ( ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
=> ( big_f(X0,X2,X0,X3)
=> ( ( big_f(X0,X3,X2,X3)
=> big_f(X0,X4,X2,X4) )
& ( big_f(X0,X4,X2,X4)
=> ( big_f(X0,X2,X0,X3)
<=> big_f(X0,X3,X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_3) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X3,X0,X4)
=> ( ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
=> ( big_f(X0,X2,X0,X3)
=> ( ( big_f(X0,X3,X2,X3)
=> big_f(X0,X4,X2,X4) )
& ( big_f(X0,X4,X2,X4)
=> ( big_f(X0,X2,X0,X3)
<=> big_f(X0,X3,X2,X3) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( ~ big_f(X0,X4,X2,X4)
& big_f(X0,X3,X2,X3) )
| ( ( big_f(X0,X2,X0,X3)
<~> big_f(X0,X3,X2,X3) )
& big_f(X0,X4,X2,X4) ) )
& big_f(X0,X2,X0,X3)
& ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
& big_f(X0,X3,X0,X4) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( ~ big_f(X0,X4,X2,X4)
& big_f(X0,X3,X2,X3) )
| ( ( big_f(X0,X2,X0,X3)
<~> big_f(X0,X3,X2,X3) )
& big_f(X0,X4,X2,X4) ) )
& big_f(X0,X2,X0,X3)
& ( big_f(X0,X2,X0,X3)
<=> big_f(X2,X1,X2,X3) )
& big_f(X0,X3,X0,X4) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( ~ big_f(X0,X4,X2,X4)
& big_f(X0,X3,X2,X3) )
| ( ( ~ big_f(X0,X3,X2,X3)
| ~ big_f(X0,X2,X0,X3) )
& ( big_f(X0,X3,X2,X3)
| big_f(X0,X2,X0,X3) )
& big_f(X0,X4,X2,X4) ) )
& big_f(X0,X2,X0,X3)
& ( big_f(X0,X2,X0,X3)
| ~ big_f(X2,X1,X2,X3) )
& ( big_f(X2,X1,X2,X3)
| ~ big_f(X0,X2,X0,X3) )
& big_f(X0,X3,X0,X4) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( ~ big_f(X0,X4,X2,X4)
& big_f(X0,X3,X2,X3) )
| ( ( ~ big_f(X0,X3,X2,X3)
| ~ big_f(X0,X2,X0,X3) )
& ( big_f(X0,X3,X2,X3)
| big_f(X0,X2,X0,X3) )
& big_f(X0,X4,X2,X4) ) )
& big_f(X0,X2,X0,X3)
& ( big_f(X0,X2,X0,X3)
| ~ big_f(X2,X1,X2,X3) )
& ( big_f(X2,X1,X2,X3)
| ~ big_f(X0,X2,X0,X3) )
& big_f(X0,X3,X0,X4) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( ( ( ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
& big_f(sK0,X3,X2,X3) )
| ( ( ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) )
& ( big_f(sK0,X3,X2,X3)
| big_f(sK0,X2,sK0,X3) )
& big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3)) ) )
& big_f(sK0,X2,sK0,X3)
& ( big_f(sK0,X2,sK0,X3)
| ~ big_f(X2,sK1,X2,X3) )
& ( big_f(X2,sK1,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) )
& big_f(sK0,X3,sK0,sK2(X2,X3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X2,X3))],[f6]) ).
fof(f11,plain,
! [X2,X3] : big_f(sK0,X2,sK0,X3),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X2,X3] :
( ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
| ~ big_f(sK0,X3,X2,X3)
| ~ big_f(sK0,X2,sK0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X2,X3] :
( ~ big_f(sK0,sK2(X2,X3),X2,sK2(X2,X3))
| ~ big_f(sK0,X3,X2,X3) ),
inference(forward_subsumption_resolution,[],[f17,f11]) ).
fof(f23,plain,
! [X0] : ~ big_f(sK0,X0,sK0,X0),
inference(resolution,[],[f21,f11]) ).
fof(f24,plain,
$false,
inference(forward_subsumption_resolution,[],[f23,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:49:40 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.74/1.15 % (3501887)Detected formulas, will run a generic FOF schedule.
% 2.74/1.15 % (3501896)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2074967669:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.15 % (3501896)First to succeed.
% 2.74/1.15 % (3501896)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3501887"
% 2.74/1.15 % (3501893)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=3218025551:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.15 % (3501892)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=2071884302:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.15 % (3501895)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2354340274:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.15 % (3501894)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=1722763134:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.15 % (3501895)Also succeeded, but the first one will report.
% 2.74/1.15 % (3501898)dis-21_1_sil=8000:lcm=predicate:random_seed=3766820471: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)
% 2.74/1.15 % (3501898)Also succeeded, but the first one will report.
% 2.74/1.15 % (3501897)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1414005589:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.15 % (3501897)Also succeeded, but the first one will report.
% 2.74/1.15 % (3501896)Refutation found. Thanks to Tanya!
% 2.74/1.15 % SZS status Theorem for theBenchmark
% 2.74/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.15 % (3501896)------------------------------
% 2.74/1.15 % (3501896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.15 % (3501896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.15 % (3501896)CaDiCaL version: 2.1.3
% 2.74/1.15 % (3501896)Termination reason: Refutation
% 2.74/1.15 % (3501896)Time elapsed: 0.001 s
% 2.74/1.15 % (3501896)Peak memory usage: 88 MB
% 2.74/1.15 % (3501896)Instructions burned: 1 (million)
% 2.74/1.15 % (3501896)------------------------------
% 2.74/1.15 % (3501896)------------------------------
% 2.74/1.15 % (3501887)Success in time 0.292 s
% 2.74/1.15 % Vampire exiting
%------------------------------------------------------------------------------