%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN328+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 02:07:19 PM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 217 ( 74 ~; 75 |; 42 &)
% ( 12 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 52 ( 42 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
! [X1,X2] :
( ( ( big_f(X1)
=> big_g(X1) )
<=> big_f(X0) )
=> ( ( ( big_f(X1)
=> big_h(X1) )
<=> big_g(X0) )
=> ( ( ( ( big_f(X1)
=> big_g(X1) )
=> big_h(X1) )
<=> big_h(X0) )
=> ( big_f(X2)
& big_g(X2)
& big_h(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_12_3) ).
fof(f2,negated_conjecture,
~ ? [X0] :
! [X1,X2] :
( ( ( big_f(X1)
=> big_g(X1) )
<=> big_f(X0) )
=> ( ( ( big_f(X1)
=> big_h(X1) )
<=> big_g(X0) )
=> ( ( ( ( big_f(X1)
=> big_g(X1) )
=> big_h(X1) )
<=> big_h(X0) )
=> ( big_f(X2)
& big_g(X2)
& big_h(X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0] :
? [X1,X2] :
( ( ~ big_f(X2)
| ~ big_g(X2)
| ~ big_h(X2) )
& ( ( big_h(X1)
| ( ~ big_g(X1)
& big_f(X1) ) )
<=> big_h(X0) )
& ( ( big_h(X1)
| ~ big_f(X1) )
<=> big_g(X0) )
& ( ( big_g(X1)
| ~ big_f(X1) )
<=> big_f(X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0] :
? [X1,X2] :
( ( ~ big_f(X2)
| ~ big_g(X2)
| ~ big_h(X2) )
& ( ( big_h(X1)
| ( ~ big_g(X1)
& big_f(X1) ) )
<=> big_h(X0) )
& ( ( big_h(X1)
| ~ big_f(X1) )
<=> big_g(X0) )
& ( ( big_g(X1)
| ~ big_f(X1) )
<=> big_f(X0) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0] :
? [X1,X2] :
( ( ~ big_f(X2)
| ~ big_g(X2)
| ~ big_h(X2) )
& ( big_h(X1)
| ( ~ big_g(X1)
& big_f(X1) )
| ~ big_h(X0) )
& ( big_h(X0)
| ( ~ big_h(X1)
& ( big_g(X1)
| ~ big_f(X1) ) ) )
& ( big_h(X1)
| ~ big_f(X1)
| ~ big_g(X0) )
& ( big_g(X0)
| ( ~ big_h(X1)
& big_f(X1) ) )
& ( big_g(X1)
| ~ big_f(X1)
| ~ big_f(X0) )
& ( big_f(X0)
| ( ~ big_g(X1)
& big_f(X1) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0] :
? [X1,X2] :
( ( ~ big_f(X2)
| ~ big_g(X2)
| ~ big_h(X2) )
& ( big_h(X1)
| ( ~ big_g(X1)
& big_f(X1) )
| ~ big_h(X0) )
& ( big_h(X0)
| ( ~ big_h(X1)
& ( big_g(X1)
| ~ big_f(X1) ) ) )
& ( big_h(X1)
| ~ big_f(X1)
| ~ big_g(X0) )
& ( big_g(X0)
| ( ~ big_h(X1)
& big_f(X1) ) )
& ( big_g(X1)
| ~ big_f(X1)
| ~ big_f(X0) )
& ( big_f(X0)
| ( ~ big_g(X1)
& big_f(X1) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ( ~ big_f(sK1(X0))
| ~ big_g(sK1(X0))
| ~ big_h(sK1(X0)) )
& ( big_h(sK0(X0))
| ( ~ big_g(sK0(X0))
& big_f(sK0(X0)) )
| ~ big_h(X0) )
& ( big_h(X0)
| ( ~ big_h(sK0(X0))
& ( big_g(sK0(X0))
| ~ big_f(sK0(X0)) ) ) )
& ( big_h(sK0(X0))
| ~ big_f(sK0(X0))
| ~ big_g(X0) )
& ( big_g(X0)
| ( ~ big_h(sK0(X0))
& big_f(sK0(X0)) ) )
& ( big_g(sK0(X0))
| ~ big_f(sK0(X0))
| ~ big_f(X0) )
& ( big_f(X0)
| ( ~ big_g(sK0(X0))
& big_f(sK0(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0))],[f6]) ).
fof(f8,plain,
! [X0] :
( big_f(sK0(X0))
| big_f(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X0] :
( ~ big_g(sK0(X0))
| big_f(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0] :
( ~ big_f(sK0(X0))
| big_g(sK0(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0] :
( big_g(X0)
| big_f(sK0(X0)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0] :
( ~ big_h(sK0(X0))
| big_g(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0] :
( ~ big_g(X0)
| ~ big_f(sK0(X0))
| big_h(sK0(X0)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0] :
( ~ big_f(sK0(X0))
| big_g(sK0(X0))
| big_h(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0] :
( ~ big_h(sK0(X0))
| big_h(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
! [X0] :
( ~ big_h(sK1(X0))
| ~ big_g(sK1(X0))
| ~ big_f(sK1(X0)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f19,plain,
! [X0] :
( big_f(sK0(sK0(X0)))
| big_f(X0) ),
inference(resolution,[],[f11,f9]) ).
fof(f26,plain,
! [X0] :
( big_g(sK0(X0))
| big_h(X0)
| big_f(X0) ),
inference(resolution,[],[f14,f8]) ).
fof(f28,plain,
! [X0] :
( big_h(X0)
| big_f(X0) ),
inference(forward_subsumption_resolution,[],[f26,f9]) ).
fof(f29,plain,
! [X0] :
( big_h(X0)
| big_f(sK0(X0)) ),
inference(resolution,[],[f28,f15]) ).
fof(f32,plain,
! [X0] :
( big_h(X0)
| big_f(sK0(sK0(X0))) ),
inference(resolution,[],[f29,f15]) ).
fof(f33,plain,
! [X0] :
( big_g(X0)
| big_f(sK0(sK0(X0))) ),
inference(resolution,[],[f29,f12]) ).
fof(f42,plain,
! [X0] :
( ~ big_g(sK1(X0))
| ~ big_f(sK1(X0))
| big_f(sK0(sK0(sK1(X0)))) ),
inference(resolution,[],[f18,f32]) ).
fof(f43,plain,
! [X0] :
( ~ big_g(sK1(X0))
| ~ big_f(sK1(X0))
| big_f(sK0(sK1(X0))) ),
inference(resolution,[],[f18,f29]) ).
fof(f45,plain,
! [X0] :
( ~ big_g(sK1(X0))
| big_f(sK0(sK1(X0))) ),
inference(forward_subsumption_resolution,[],[f43,f8]) ).
fof(f46,plain,
! [X0] :
( ~ big_g(sK1(X0))
| big_f(sK0(sK0(sK1(X0)))) ),
inference(forward_subsumption_resolution,[],[f42,f19]) ).
fof(f47,plain,
! [X0] : big_f(sK0(sK1(X0))),
inference(forward_subsumption_resolution,[],[f45,f11]) ).
fof(f48,plain,
! [X0] : big_f(sK0(sK0(sK1(X0)))),
inference(forward_subsumption_resolution,[],[f46,f33]) ).
fof(f55,plain,
! [X0] :
( big_g(sK0(sK0(sK1(X0))))
| ~ big_f(sK0(sK1(X0))) ),
inference(resolution,[],[f48,f10]) ).
fof(f56,plain,
! [X0] : big_g(sK0(sK0(sK1(X0)))),
inference(forward_subsumption_resolution,[],[f55,f47]) ).
fof(f60,plain,
! [X0] :
( ~ big_f(sK0(sK0(sK0(sK1(X0)))))
| big_h(sK0(sK0(sK0(sK1(X0))))) ),
inference(resolution,[],[f56,f13]) ).
fof(f61,plain,
! [X0] : big_h(sK0(sK0(sK0(sK1(X0))))),
inference(forward_subsumption_resolution,[],[f60,f28]) ).
fof(f76,plain,
! [X0] : big_h(sK0(sK0(sK1(X0)))),
inference(resolution,[],[f61,f15]) ).
fof(f83,plain,
! [X0] : big_h(sK0(sK1(X0))),
inference(resolution,[],[f76,f15]) ).
fof(f84,plain,
! [X0] : big_g(sK0(sK1(X0))),
inference(resolution,[],[f76,f12]) ).
fof(f87,plain,
! [X0] : big_h(sK1(X0)),
inference(resolution,[],[f83,f15]) ).
fof(f88,plain,
! [X0] : big_g(sK1(X0)),
inference(resolution,[],[f83,f12]) ).
fof(f96,plain,
! [X0] :
( ~ big_g(sK1(X0))
| ~ big_f(sK1(X0)) ),
inference(resolution,[],[f87,f18]) ).
fof(f99,plain,
! [X0] : ~ big_f(sK1(X0)),
inference(forward_subsumption_resolution,[],[f96,f88]) ).
fof(f115,plain,
! [X0] : big_f(sK1(X0)),
inference(resolution,[],[f84,f9]) ).
fof(f117,plain,
$false,
inference(forward_subsumption_resolution,[],[f115,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN328+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 15:45:32 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.28 % (2736057)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (2736071)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1899061178:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (2736071) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2736057-2736071"...
% 0.19/0.28 % (2736071)...printing done.
% 0.19/0.28 % (2736067)% WARNING: option uhcvi not known.
% 0.19/0.28 % (2736067)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=88626785:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (2736069)dis+10_1_sil=32000:sp=arity:random_seed=3511320138:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (2736070)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3743523641:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (2736071)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (2736071)------------------------------
% 0.19/0.28 % (2736071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2736071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2736071)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2736071)Termination reason: Refutation
% 0.19/0.28 % (2736071)Time elapsed: 0.002 s
% 0.19/0.28 % (2736071)Peak memory usage: 11 MB
% 0.19/0.28 % (2736071)Instructions burned: 3 (million)
% 0.19/0.28 % (2736057)Success in time 0.044 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------