%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN321+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 : n005.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 01:50:11 PM UTC 2026
% Result : Theorem 3.55s 1.34s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 85 ( 28 ~; 24 |; 16 &)
% ( 3 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 72 ( 60 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X2] : big_g(X0,X2) )
=> ( ! [X2] :
( big_g(X2,X2)
=> big_f(X2,X1) )
=> ( big_f(X0,X1)
<=> ! [X2] : big_g(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_3_2) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X2] : big_g(X0,X2) )
=> ( ! [X2] :
( big_g(X2,X2)
=> big_f(X2,X1) )
=> ( big_f(X0,X1)
<=> ! [X2] : big_g(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ? [X0,X1] :
( ( ? [X2] : big_f(X0,X2)
=> ! [X3] : big_g(X0,X3) )
=> ( ! [X4] :
( big_g(X4,X4)
=> big_f(X4,X1) )
=> ( big_f(X0,X1)
<=> ! [X5] : big_g(X0,X5) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
( ( big_f(X0,X1)
<~> ! [X5] : big_g(X0,X5) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X3] : big_g(X0,X3)
| ! [X2] : ~ big_f(X0,X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ( big_f(X0,X1)
<~> ! [X5] : big_g(X0,X5) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X3] : big_g(X0,X3)
| ! [X2] : ~ big_f(X0,X2) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( ( ? [X5] : ~ big_g(X0,X5)
| ~ big_f(X0,X1) )
& ( ! [X5] : big_g(X0,X5)
| big_f(X0,X1) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X3] : big_g(X0,X3)
| ! [X2] : ~ big_f(X0,X2) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( ? [X5] : ~ big_g(X0,X5)
| ~ big_f(X0,X1) )
& ( ! [X5] : big_g(X0,X5)
| big_f(X0,X1) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X3] : big_g(X0,X3)
| ! [X2] : ~ big_f(X0,X2) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ( ? [X2] : ~ big_g(X0,X2)
| ~ big_f(X0,X1) )
& ( ! [X3] : big_g(X0,X3)
| big_f(X0,X1) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X5] : big_g(X0,X5)
| ! [X6] : ~ big_f(X0,X6) ) ),
inference(rectify,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ( ~ big_g(X0,sK0(X0))
| ~ big_f(X0,X1) )
& ( ! [X3] : big_g(X0,X3)
| big_f(X0,X1) )
& ! [X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) )
& ( ! [X5] : big_g(X0,X5)
| ! [X6] : ~ big_f(X0,X6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f8]) ).
fof(f10,plain,
! [X0,X6,X5] :
( big_g(X0,X5)
| ~ big_f(X0,X6) ),
inference(cnf_transformation,[],[f9]) ).
fof(f11,plain,
! [X1,X4] :
( big_f(X4,X1)
| ~ big_g(X4,X4) ),
inference(cnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X3,X0,X1] :
( big_g(X0,X3)
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( ~ big_g(X0,sK0(X0))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f14,plain,
! [X3,X0] : big_g(X0,X3),
inference(forward_subsumption_resolution,[],[f12,f10]) ).
fof(f15,plain,
! [X0,X1] : ~ big_f(X0,X1),
inference(forward_subsumption_resolution,[],[f13,f14]) ).
fof(f16,plain,
! [X0] : ~ big_g(X0,X0),
inference(resolution,[],[f15,f11]) ).
fof(f17,plain,
$false,
inference(forward_subsumption_resolution,[],[f16,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN321+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 15:41:51 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running first-order theorem proving
% 0.09/0.25 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
% 3.55/1.34 % (889324)Detected formulas, will run a generic FOF schedule.
% 3.55/1.34 % (889374)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=2023970347:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 3.55/1.34 % (889375)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=1540967151:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 3.55/1.34 % (889381)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1079223370:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 3.55/1.34 % (889380)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=411763945:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 3.55/1.34 % (889380)First to succeed.
% 3.55/1.34 % (889381)Also succeeded, but the first one will report.
% 3.55/1.34 % (889380)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-889324"
% 3.55/1.34 % (889378)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=2390458034:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 3.55/1.34 % (889379)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=152907394:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 3.55/1.34 % (889379)Also succeeded, but the first one will report.
% 3.55/1.34 % (889382)dis-21_1_sil=8000:lcm=predicate:random_seed=908001313: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)
% 3.55/1.34 % (889382)Also succeeded, but the first one will report.
% 3.55/1.34 % (889380)Refutation found. Thanks to Tanya!
% 3.55/1.34 % SZS status Theorem for theBenchmark
% 3.55/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.34 % (889380)------------------------------
% 3.55/1.34 % (889380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.34 % (889380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.34 % (889380)CaDiCaL version: 2.1.3
% 3.55/1.34 % (889380)Termination reason: Refutation
% 3.55/1.34 % (889380)Time elapsed: 0.002 s
% 3.55/1.34 % (889380)Peak memory usage: 88 MB
% 3.55/1.34 % (889380)Instructions burned: 1 (million)
% 3.55/1.34 % (889380)------------------------------
% 3.55/1.34 % (889380)------------------------------
% 3.55/1.34 % (889324)Success in time 0.393 s
% 3.55/1.34 % Vampire exiting
%------------------------------------------------------------------------------