%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 02:07:20 PM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 4 unt; 0 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 215 ( 60 ~; 70 |; 51 &)
% ( 18 <=>; 10 =>; 0 <=; 6 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 54 ( 46 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
! [X2] :
( ( ( big_f(X0,X1)
& big_f(X1,X0) )
<~> big_f(X0,X2) )
=> ( ( big_f(X0,X2)
<=> big_f(X2,X0) )
=> ( ( big_f(X0,X2)
<=> big_f(X1,X2) )
=> ( ( ( big_f(X1,X0)
=> big_f(X0,X1) )
<=> big_f(X2,X2) )
=> ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<=> big_f(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_4) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
! [X2] :
( ( ( big_f(X0,X1)
& big_f(X1,X0) )
<~> big_f(X0,X2) )
=> ( ( big_f(X0,X2)
<=> big_f(X2,X0) )
=> ( ( big_f(X0,X2)
<=> big_f(X1,X2) )
=> ( ( ( big_f(X1,X0)
=> big_f(X0,X1) )
<=> big_f(X2,X2) )
=> ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<=> big_f(X2,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0,X1] :
? [X2] :
( ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<~> big_f(X2,X1) )
& ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
<=> big_f(X2,X2) )
& ( big_f(X0,X2)
<=> big_f(X1,X2) )
& ( big_f(X0,X2)
<=> big_f(X2,X0) )
& ( ( big_f(X0,X1)
& big_f(X1,X0) )
<~> big_f(X0,X2) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
? [X2] :
( ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<~> big_f(X2,X1) )
& ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
<=> big_f(X2,X2) )
& ( big_f(X0,X2)
<=> big_f(X1,X2) )
& ( big_f(X0,X2)
<=> big_f(X2,X0) )
& ( ( big_f(X0,X1)
& big_f(X1,X0) )
<~> big_f(X0,X2) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
? [X2] :
( ( ~ big_f(X2,X1)
| ( ( ~ big_f(X1,X0)
| ~ big_f(X0,X1) )
& ( big_f(X1,X0)
| big_f(X0,X1) ) ) )
& ( big_f(X2,X1)
| ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X1,X0)
| ~ big_f(X0,X1) ) ) )
& ( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(X2,X2) )
& ( big_f(X2,X2)
| ( ~ big_f(X0,X1)
& big_f(X1,X0) ) )
& ( big_f(X0,X2)
| ~ big_f(X1,X2) )
& ( big_f(X1,X2)
| ~ big_f(X0,X2) )
& ( big_f(X0,X2)
| ~ big_f(X2,X0) )
& ( big_f(X2,X0)
| ~ big_f(X0,X2) )
& ( ~ big_f(X0,X2)
| ~ big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X0,X2)
| ( big_f(X0,X1)
& big_f(X1,X0) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
? [X2] :
( ( ~ big_f(X2,X1)
| ( ( ~ big_f(X1,X0)
| ~ big_f(X0,X1) )
& ( big_f(X1,X0)
| big_f(X0,X1) ) ) )
& ( big_f(X2,X1)
| ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X1,X0)
| ~ big_f(X0,X1) ) ) )
& ( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(X2,X2) )
& ( big_f(X2,X2)
| ( ~ big_f(X0,X1)
& big_f(X1,X0) ) )
& ( big_f(X0,X2)
| ~ big_f(X1,X2) )
& ( big_f(X1,X2)
| ~ big_f(X0,X2) )
& ( big_f(X0,X2)
| ~ big_f(X2,X0) )
& ( big_f(X2,X0)
| ~ big_f(X0,X2) )
& ( ~ big_f(X0,X2)
| ~ big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X0,X2)
| ( big_f(X0,X1)
& big_f(X1,X0) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( ~ big_f(sK0(X0,X1),X1)
| ( ( ~ big_f(X1,X0)
| ~ big_f(X0,X1) )
& ( big_f(X1,X0)
| big_f(X0,X1) ) ) )
& ( big_f(sK0(X0,X1),X1)
| ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X1,X0)
| ~ big_f(X0,X1) ) ) )
& ( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) )
& ( big_f(sK0(X0,X1),sK0(X0,X1))
| ( ~ big_f(X0,X1)
& big_f(X1,X0) ) )
& ( big_f(X0,sK0(X0,X1))
| ~ big_f(X1,sK0(X0,X1)) )
& ( big_f(X1,sK0(X0,X1))
| ~ big_f(X0,sK0(X0,X1)) )
& ( big_f(X0,sK0(X0,X1))
| ~ big_f(sK0(X0,X1),X0) )
& ( big_f(sK0(X0,X1),X0)
| ~ big_f(X0,sK0(X0,X1)) )
& ( ~ big_f(X0,sK0(X0,X1))
| ~ big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X0,sK0(X0,X1))
| ( big_f(X0,X1)
& big_f(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_f(X0,sK0(X0,X1))
| big_f(X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( big_f(X0,sK0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_f(X0,sK0(X0,X1))
| big_f(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( ~ big_f(X0,sK0(X0,X1))
| big_f(X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0,X1] :
( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( ~ big_f(sK0(X0,X1),X1)
| big_f(X1,X0)
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X0,X1] :
( ~ big_f(sK0(X0,X1),X1)
| ~ big_f(X1,X0)
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1] :
( big_f(sK0(X0,X1),X0)
| big_f(X0,X1) ),
inference(resolution,[],[f11,f9]) ).
fof(f26,plain,
! [X0,X1] :
( big_f(X0,sK0(X1,X0))
| big_f(X0,X1) ),
inference(resolution,[],[f13,f8]) ).
fof(f45,plain,
! [X0] :
( big_f(X0,X0)
| big_f(X0,X0)
| big_f(X0,X0) ),
inference(resolution,[],[f20,f22]) ).
fof(f50,plain,
! [X0] : big_f(X0,X0),
inference(duplicate_literal_removal,[],[f45]) ).
fof(f60,plain,
! [X0,X1] :
( ~ big_f(X1,X0)
| big_f(X0,X1) ),
inference(forward_subsumption_resolution,[],[f17,f50]) ).
fof(f63,plain,
! [X0,X1] :
( big_f(sK0(X0,X1),X1)
| big_f(X1,X0) ),
inference(resolution,[],[f60,f26]) ).
fof(f75,plain,
! [X0,X1] :
( big_f(X0,X1)
| big_f(X0,X1)
| big_f(X1,X0) ),
inference(resolution,[],[f63,f20]) ).
fof(f77,plain,
! [X0,X1] :
( big_f(X0,X1)
| big_f(X1,X0) ),
inference(duplicate_literal_removal,[],[f75]) ).
fof(f78,plain,
! [X0,X1] : big_f(X0,X1),
inference(forward_subsumption_resolution,[],[f77,f60]) ).
fof(f85,plain,
! [X0,X1] :
( ~ big_f(X0,X1)
| ~ big_f(X1,X0) ),
inference(resolution,[],[f78,f21]) ).
fof(f87,plain,
! [X0,X1] : ~ big_f(X1,X0),
inference(forward_subsumption_resolution,[],[f85,f60]) ).
fof(f89,plain,
$false,
inference(forward_subsumption_resolution,[],[f87,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.16 % Computer : n013.cluster.edu
% 0.06/0.16 % Model : x86_64 x86_64
% 0.06/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.16 % Memory : 8046.5625MB
% 0.06/0.16 % OS : Linux 6.8.0-71-generic
% 0.06/0.16 % CPULimit : 300
% 0.06/0.16 % WCLimit : 300
% 0.06/0.16 % DateTime : Mon Sep 28 15:42:07 UTC 2026
% 0.06/0.16 % CPUTime :
% 0.06/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.25 % (1289236)Will run a generic schedule for satisfiability detection.
% 0.06/0.25 % (1289241)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2849585575_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.25 % TRYING [1]
% 0.06/0.25 % TRYING [2]
% 0.06/0.25 % TRYING [3]
% 0.06/0.25 % TRYING [4]
% 0.06/0.25 % TRYING [5]
% 0.06/0.25 % (1289242)% WARNING: option uhcvi not known.
% 0.06/0.25 % TRYING [6]
% 0.06/0.25 % TRYING [7]
% 0.06/0.25 % (1289243)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=379372416:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.25 % (1289244)dis+10_1_sil=32000:sp=arity:random_seed=315849550:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.25 % (1289247)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=673876795:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.25 % (1289246)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3906842757:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.25 % (1289242)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1286636175:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.25 % (1289245)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=529327521:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.25 % (1289244) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1289236-1289244"...
% 0.06/0.25 % (1289242) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1289236-1289242"...
% 0.06/0.25 % (1289245) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1289236-1289245"...
% 0.06/0.25 % (1289246) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1289236-1289246"...
% 0.06/0.25 % (1289244)...printing done.
% 0.06/0.25 % (1289247) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1289236-1289247"...
% 0.06/0.25 % (1289243) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1289236-1289243"...
% 0.06/0.25 % (1289245)...printing done.
% 0.06/0.25 % (1289242)...printing done.
% 0.06/0.25 % (1289246)...printing done.
% 0.06/0.25 % (1289244)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.25 % (1289244)------------------------------
% 0.06/0.25 % (1289244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.25 % (1289244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.25 % (1289244)CaDiCaL version: 2.1.3
% 0.06/0.25 % (1289244)Termination reason: Refutation
% 0.06/0.25 % (1289244)Time elapsed: 0.002 s
% 0.06/0.25 % (1289244)Peak memory usage: 11 MB
% 0.06/0.25 % (1289244)Instructions burned: 2 (million)
% 0.06/0.25 % (1289236)Success in time 0.039 s
% 0.06/0.25 % Vampire exiting
%------------------------------------------------------------------------------