%------------------------------------------------------------------------------
% File : Vampire---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 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 01:50:13 PM UTC 2026
% Result : Theorem 3.61s 1.19s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 210 ( 72 ~; 70 |; 42 &)
% ( 12 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 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 : 40 ( 30 !; 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(f12,plain,
! [X0] :
( ~ big_h(sK0(X0))
| big_g(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0] :
( big_h(sK0(X0))
| ~ big_f(sK0(X0))
| ~ big_g(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0] :
( big_g(sK0(X0))
| big_h(X0)
| ~ big_f(sK0(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_f(sK1(X0))
| ~ big_g(sK1(X0))
| ~ big_h(sK1(X0)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0] :
( ~ big_f(sK0(X0))
| ~ big_g(X0)
| big_h(X0) ),
inference(resolution,[],[f13,f15]) ).
fof(f24,plain,
! [X0] :
( big_h(X0)
| ~ big_f(sK0(X0))
| big_f(X0) ),
inference(resolution,[],[f14,f9]) ).
fof(f25,plain,
! [X0] :
( big_h(X0)
| big_f(X0) ),
inference(forward_subsumption_resolution,[],[f24,f8]) ).
fof(f26,plain,
! [X0] :
( big_f(sK0(X0))
| big_h(X0) ),
inference(resolution,[],[f25,f15]) ).
fof(f28,plain,
! [X0] :
( big_h(X0)
| ~ big_g(X0)
| big_h(X0) ),
inference(resolution,[],[f26,f20]) ).
fof(f29,plain,
! [X0] :
( big_h(X0)
| ~ big_g(X0) ),
inference(duplicate_literal_removal,[],[f28]) ).
fof(f31,plain,
! [X0] :
( ~ big_g(sK0(X0))
| big_h(X0) ),
inference(resolution,[],[f29,f15]) ).
fof(f33,plain,
! [X0] :
( big_h(X0)
| big_h(X0)
| ~ big_f(sK0(X0)) ),
inference(resolution,[],[f31,f14]) ).
fof(f35,plain,
! [X0] :
( big_h(X0)
| ~ big_f(sK0(X0)) ),
inference(duplicate_literal_removal,[],[f33]) ).
fof(f37,plain,
! [X0] : big_h(X0),
inference(forward_subsumption_resolution,[],[f35,f26]) ).
fof(f40,plain,
! [X0] : big_g(X0),
inference(resolution,[],[f37,f12]) ).
fof(f41,plain,
! [X0] :
( ~ big_g(sK1(X0))
| ~ big_f(sK1(X0)) ),
inference(forward_subsumption_resolution,[],[f18,f37]) ).
fof(f43,plain,
! [X0] : big_f(X0),
inference(resolution,[],[f40,f9]) ).
fof(f44,plain,
! [X0] : ~ big_f(sK1(X0)),
inference(resolution,[],[f40,f41]) ).
fof(f46,plain,
$false,
inference(forward_subsumption_resolution,[],[f44,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN328+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n002.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 15:44:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.61/1.19 % (470140)Detected formulas, will run a generic FOF schedule.
% 3.61/1.19 % (470146)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=3468159223:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.61/1.19 % (470145)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=1168503127:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.61/1.19 % (470147)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=4266760078:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.61/1.19 % (470150)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2903228997:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.61/1.19 % (470148)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=341083002:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.61/1.19 % (470151)dis-21_1_sil=8000:lcm=predicate:random_seed=2144085235: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)
% 3.61/1.19 % (470149)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4126063168:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.61/1.19 % (470149)First to succeed.
% 3.61/1.19 % (470150)Also succeeded, but the first one will report.
% 3.61/1.19 % (470148)Also succeeded, but the first one will report.
% 3.61/1.19 % (470149)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-470140"
% 3.61/1.19 % (470151)Also succeeded, but the first one will report.
% 3.61/1.19 % (470149)Refutation found. Thanks to Tanya!
% 3.61/1.19 % SZS status Theorem for theBenchmark
% 3.61/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.19 % (470149)------------------------------
% 3.61/1.19 % (470149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.19 % (470149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.19 % (470149)CaDiCaL version: 2.1.3
% 3.61/1.19 % (470149)Termination reason: Refutation
% 3.61/1.19 % (470149)Time elapsed: 0.002 s
% 3.61/1.19 % (470149)Peak memory usage: 88 MB
% 3.61/1.19 % (470149)Instructions burned: 1 (million)
% 3.61/1.19 % (470149)------------------------------
% 3.61/1.19 % (470149)------------------------------
% 3.61/1.19 % (470140)Success in time 0.436 s
% 3.61/1.19 % Vampire exiting
%------------------------------------------------------------------------------