%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN350+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 : n003.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 01:50:19 PM UTC 2026
% Result : Theorem 3.61s 1.29s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 83 ( 29 ~; 25 |; 19 &)
% ( 5 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 35 ( 25 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
? [X1,X2] :
! [X3] :
( ( big_f(X0,X3)
<=> big_f(X3,X0) )
=> ( big_f(X0,X3)
<=> ( big_f(X2,X3)
& ( big_f(X1,X3)
=> big_f(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_18_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
! [X3] :
( ( big_f(X0,X3)
<=> big_f(X3,X0) )
=> ( big_f(X0,X3)
<=> ( big_f(X2,X3)
& ( big_f(X1,X3)
=> big_f(X1,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
! [X1,X2] :
? [X3] :
( ( big_f(X0,X3)
<~> ( big_f(X2,X3)
& ( big_f(X1,X2)
| ~ big_f(X1,X3) ) ) )
& ( big_f(X0,X3)
<=> big_f(X3,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1,X2] :
? [X3] :
( ( ~ big_f(X2,X3)
| ( ~ big_f(X1,X2)
& big_f(X1,X3) )
| ~ big_f(X0,X3) )
& ( ( big_f(X2,X3)
& ( big_f(X1,X2)
| ~ big_f(X1,X3) ) )
| big_f(X0,X3) )
& ( big_f(X0,X3)
| ~ big_f(X3,X0) )
& ( big_f(X3,X0)
| ~ big_f(X0,X3) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
! [X1,X2] :
? [X3] :
( ( ~ big_f(X2,X3)
| ( ~ big_f(X1,X2)
& big_f(X1,X3) )
| ~ big_f(X0,X3) )
& ( ( big_f(X2,X3)
& ( big_f(X1,X2)
| ~ big_f(X1,X3) ) )
| big_f(X0,X3) )
& ( big_f(X0,X3)
| ~ big_f(X3,X0) )
& ( big_f(X3,X0)
| ~ big_f(X0,X3) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X1,X2] :
( ( ~ big_f(X2,sK1(X1,X2))
| ( ~ big_f(X1,X2)
& big_f(X1,sK1(X1,X2)) )
| ~ big_f(sK0,sK1(X1,X2)) )
& ( ( big_f(X2,sK1(X1,X2))
& ( big_f(X1,X2)
| ~ big_f(X1,sK1(X1,X2)) ) )
| big_f(sK0,sK1(X1,X2)) )
& ( big_f(sK0,sK1(X1,X2))
| ~ big_f(sK1(X1,X2),sK0) )
& ( big_f(sK1(X1,X2),sK0)
| ~ big_f(sK0,sK1(X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1(X1,X2))],[f5]) ).
fof(f7,plain,
! [X2,X1] :
( big_f(sK1(X1,X2),sK0)
| ~ big_f(sK0,sK1(X1,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X1] :
( big_f(sK0,sK1(X1,X2))
| big_f(X2,sK1(X1,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
! [X2,X1] :
( ~ big_f(sK0,sK1(X1,X2))
| ~ big_f(X1,X2)
| ~ big_f(X2,sK1(X1,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f16,plain,
! [X0] :
( ~ big_f(sK0,sK1(X0,sK0))
| ~ big_f(X0,sK0) ),
inference(factoring,[],[f12]) ).
fof(f18,plain,
! [X0] :
( ~ big_f(X0,sK0)
| big_f(sK0,sK1(X0,sK0)) ),
inference(resolution,[],[f16,f10]) ).
fof(f20,plain,
! [X0] : ~ big_f(X0,sK0),
inference(forward_subsumption_resolution,[],[f18,f16]) ).
fof(f25,plain,
! [X0,X1] : ~ big_f(sK0,sK1(X0,X1)),
inference(resolution,[],[f20,f7]) ).
fof(f27,plain,
! [X0,X1] : big_f(X0,sK1(X1,X0)),
inference(resolution,[],[f25,f10]) ).
fof(f31,plain,
$false,
inference(resolution,[],[f27,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN350+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n003.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 15:49:12 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running first-order theorem proving
% 0.11/0.22 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
% 3.61/1.29 % (1717443)Detected formulas, will run a generic FOF schedule.
% 3.61/1.29 % (1717450)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=3237134591:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.61/1.29 % (1717453)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3043186243:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.61/1.29 % (1717451)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3564700760:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.61/1.29 % (1717449)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=3507302764:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.61/1.29 % (1717454)dis-21_1_sil=8000:lcm=predicate:random_seed=4197086574: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)
% 3.61/1.29 % (1717448)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=3404280167:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.61/1.29 % (1717452)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1389104614:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.61/1.29 % (1717452)First to succeed.
% 3.61/1.29 % (1717451)Also succeeded, but the first one will report.
% 3.61/1.29 % (1717454)Also succeeded, but the first one will report.
% 3.61/1.29 % (1717453)Also succeeded, but the first one will report.
% 3.61/1.29 % (1717452)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1717443"
% 3.61/1.29 % (1717452)Refutation found. Thanks to Tanya!
% 3.61/1.29 % SZS status Theorem for theBenchmark
% 3.61/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.29 % (1717452)------------------------------
% 3.61/1.29 % (1717452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.29 % (1717452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.29 % (1717452)CaDiCaL version: 2.1.3
% 3.61/1.29 % (1717452)Termination reason: Refutation
% 3.61/1.29 % (1717452)Time elapsed: 0.002 s
% 3.61/1.29 % (1717452)Peak memory usage: 88 MB
% 3.61/1.29 % (1717452)Instructions burned: 1 (million)
% 3.61/1.29 % (1717452)------------------------------
% 3.61/1.29 % (1717452)------------------------------
% 3.61/1.29 % (1717443)Success in time 0.43 s
% 3.61/1.29 % Vampire exiting
%------------------------------------------------------------------------------