%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN317+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 : n011.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 01:50:10 PM UTC 2026
% Result : Theorem 0.22s 1.13s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 69 ( 27 ~; 23 |; 9 &)
% ( 3 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 34 ( 16 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
( big_f(X0)
=> big_g(X0) )
<=> ? [X0,X1] :
( big_f(X0)
=> big_g(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_2_3) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( big_f(X0)
=> big_g(X0) )
<=> ? [X0,X1] :
( big_f(X0)
=> big_g(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
( big_f(X0)
=> big_g(X0) )
<=> ? [X1,X2] :
( big_f(X1)
=> big_g(X2) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
( big_g(X0)
| ~ big_f(X0) )
<~> ? [X1,X2] :
( big_g(X2)
| ~ big_f(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ! [X1,X2] :
( ~ big_g(X2)
& big_f(X1) )
| ! [X0] :
( ~ big_g(X0)
& big_f(X0) ) )
& ( ? [X1,X2] :
( big_g(X2)
| ~ big_f(X1) )
| ? [X0] :
( big_g(X0)
| ~ big_f(X0) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ! [X0,X1] :
( ~ big_g(X1)
& big_f(X0) )
| ! [X2] :
( ~ big_g(X2)
& big_f(X2) ) )
& ( ? [X3,X4] :
( big_g(X4)
| ~ big_f(X3) )
| ? [X5] :
( big_g(X5)
| ~ big_f(X5) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ! [X0,X1] :
( ~ big_g(X1)
& big_f(X0) )
| ! [X2] :
( ~ big_g(X2)
& big_f(X2) ) )
& ( big_g(sK1)
| ~ big_f(sK0)
| big_g(sK2)
| ~ big_f(sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f6]) ).
fof(f8,plain,
( big_g(sK1)
| ~ big_f(sK0)
| big_g(sK2)
| ~ big_f(sK2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X0] :
( big_f(X2)
| big_f(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X1] :
( ~ big_g(X2)
| ~ big_g(X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0] : ~ big_g(X0),
inference(factoring,[],[f12]) ).
fof(f14,plain,
( ~ big_f(sK0)
| big_g(sK2)
| ~ big_f(sK2) ),
inference(forward_subsumption_resolution,[],[f8,f13]) ).
fof(f15,plain,
( ~ big_f(sK2)
| ~ big_f(sK0) ),
inference(forward_subsumption_resolution,[],[f14,f13]) ).
fof(f17,plain,
! [X0] :
( ~ big_f(sK0)
| big_f(X0) ),
inference(resolution,[],[f15,f9]) ).
fof(f18,plain,
! [X0] : big_f(X0),
inference(forward_subsumption_resolution,[],[f17,f9]) ).
fof(f19,plain,
~ big_f(sK0),
inference(resolution,[],[f18,f15]) ).
fof(f20,plain,
$false,
inference(forward_subsumption_resolution,[],[f19,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN317+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n011.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 15:42:05 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 0.22/1.13 % (3486233)Detected formulas, will run a generic FOF schedule.
% 0.22/1.13 % (3486289)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1542227544:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 0.22/1.13 % (3486289)First to succeed.
% 0.22/1.13 % (3486289)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3486233"
% 0.22/1.13 % (3486288)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1039451562:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 0.22/1.13 % (3486287)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=3979567300:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 0.22/1.13 % (3486288)Also succeeded, but the first one will report.
% 0.22/1.13 % (3486286)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=1296693142:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 0.22/1.13 % (3486285)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=1696425517:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 0.22/1.13 % (3486291)dis-21_1_sil=8000:lcm=predicate:random_seed=2802626520:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 0.22/1.13 % (3486290)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1409756161:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 0.22/1.13 % (3486291)Also succeeded, but the first one will report.
% 0.22/1.13 % (3486290)Also succeeded, but the first one will report.
% 0.22/1.13 % (3486289)Refutation found. Thanks to Tanya!
% 0.22/1.13 % SZS status Theorem for theBenchmark
% 0.22/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/1.13 % (3486289)------------------------------
% 0.22/1.13 % (3486289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.13 % (3486289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.13 % (3486289)CaDiCaL version: 2.1.3
% 0.22/1.13 % (3486289)Termination reason: Refutation
% 0.22/1.13 % (3486289)Time elapsed: 0.001 s
% 0.22/1.13 % (3486289)Peak memory usage: 88 MB
% 0.22/1.13 % (3486289)------------------------------
% 0.22/1.13 % (3486289)------------------------------
% 0.22/1.13 % (3486233)Success in time 0.265 s
% 0.22/1.13 % Vampire exiting
%------------------------------------------------------------------------------