%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN332+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 : n017.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 01:50:14 PM UTC 2026
% Result : Theorem 5.10s 1.78s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 242 ( 82 ~; 75 |; 51 &)
% ( 18 <=>; 10 =>; 0 <=; 6 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 56 ( 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0,X1] :
! [X2] :
( ( ( big_f(X0,X1)
& big_f(X1,X0) )
<~> big_f(X0,X2) )
=> ( ( big_f(X0,X2)
<=> big_f(X2,X0) )
=> ( ( big_f(X0,X2)
<=> big_f(X1,X2) )
=> ( ( ( big_f(X1,X0)
=> big_f(X0,X1) )
<=> big_f(X2,X2) )
=> ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<=> big_f(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_4) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
! [X2] :
( ( ( big_f(X0,X1)
& big_f(X1,X0) )
<~> big_f(X0,X2) )
=> ( ( big_f(X0,X2)
<=> big_f(X2,X0) )
=> ( ( big_f(X0,X2)
<=> big_f(X1,X2) )
=> ( ( ( big_f(X1,X0)
=> big_f(X0,X1) )
<=> big_f(X2,X2) )
=> ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<=> big_f(X2,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0,X1] :
? [X2] :
( ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<~> big_f(X2,X1) )
& ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
<=> big_f(X2,X2) )
& ( big_f(X0,X2)
<=> big_f(X1,X2) )
& ( big_f(X0,X2)
<=> big_f(X2,X0) )
& ( ( big_f(X0,X1)
& big_f(X1,X0) )
<~> big_f(X0,X2) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0,X1] :
? [X2] :
( ( ( big_f(X0,X1)
<=> big_f(X1,X0) )
<~> big_f(X2,X1) )
& ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
<=> big_f(X2,X2) )
& ( big_f(X0,X2)
<=> big_f(X1,X2) )
& ( big_f(X0,X2)
<=> big_f(X2,X0) )
& ( ( big_f(X0,X1)
& big_f(X1,X0) )
<~> big_f(X0,X2) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
? [X2] :
( ( ~ big_f(X2,X1)
| ( ( ~ big_f(X1,X0)
| ~ big_f(X0,X1) )
& ( big_f(X1,X0)
| big_f(X0,X1) ) ) )
& ( big_f(X2,X1)
| ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X1,X0)
| ~ big_f(X0,X1) ) ) )
& ( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(X2,X2) )
& ( big_f(X2,X2)
| ( ~ big_f(X0,X1)
& big_f(X1,X0) ) )
& ( big_f(X0,X2)
| ~ big_f(X1,X2) )
& ( big_f(X1,X2)
| ~ big_f(X0,X2) )
& ( big_f(X0,X2)
| ~ big_f(X2,X0) )
& ( big_f(X2,X0)
| ~ big_f(X0,X2) )
& ( ~ big_f(X0,X2)
| ~ big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X0,X2)
| ( big_f(X0,X1)
& big_f(X1,X0) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
? [X2] :
( ( ~ big_f(X2,X1)
| ( ( ~ big_f(X1,X0)
| ~ big_f(X0,X1) )
& ( big_f(X1,X0)
| big_f(X0,X1) ) ) )
& ( big_f(X2,X1)
| ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X1,X0)
| ~ big_f(X0,X1) ) ) )
& ( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(X2,X2) )
& ( big_f(X2,X2)
| ( ~ big_f(X0,X1)
& big_f(X1,X0) ) )
& ( big_f(X0,X2)
| ~ big_f(X1,X2) )
& ( big_f(X1,X2)
| ~ big_f(X0,X2) )
& ( big_f(X0,X2)
| ~ big_f(X2,X0) )
& ( big_f(X2,X0)
| ~ big_f(X0,X2) )
& ( ~ big_f(X0,X2)
| ~ big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X0,X2)
| ( big_f(X0,X1)
& big_f(X1,X0) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( ~ big_f(sK0(X0,X1),X1)
| ( ( ~ big_f(X1,X0)
| ~ big_f(X0,X1) )
& ( big_f(X1,X0)
| big_f(X0,X1) ) ) )
& ( big_f(sK0(X0,X1),X1)
| ( ( big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X1,X0)
| ~ big_f(X0,X1) ) ) )
& ( big_f(X0,X1)
| ~ big_f(X1,X0)
| ~ big_f(sK0(X0,X1),sK0(X0,X1)) )
& ( big_f(sK0(X0,X1),sK0(X0,X1))
| ( ~ big_f(X0,X1)
& big_f(X1,X0) ) )
& ( big_f(X0,sK0(X0,X1))
| ~ big_f(X1,sK0(X0,X1)) )
& ( big_f(X1,sK0(X0,X1))
| ~ big_f(X0,sK0(X0,X1)) )
& ( big_f(X0,sK0(X0,X1))
| ~ big_f(sK0(X0,X1),X0) )
& ( big_f(sK0(X0,X1),X0)
| ~ big_f(X0,sK0(X0,X1)) )
& ( ~ big_f(X0,sK0(X0,X1))
| ~ big_f(X0,X1)
| ~ big_f(X1,X0) )
& ( big_f(X0,sK0(X0,X1))
| ( big_f(X0,X1)
& big_f(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_f(X0,sK0(X0,X1))
| big_f(X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( big_f(X0,sK0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ~ big_f(X0,sK0(X0,X1))
| ~ big_f(X0,X1)
| ~ big_f(X1,X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( big_f(sK0(X0,X1),X0)
| ~ big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( big_f(X0,sK0(X0,X1))
| ~ big_f(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( big_f(X1,sK0(X0,X1))
| ~ big_f(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1] :
( big_f(X0,sK0(X0,X1))
| ~ big_f(X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0,X1] :
( ~ big_f(sK0(X0,X1),sK0(X0,X1))
| ~ big_f(X1,X0)
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( big_f(X1,X0)
| ~ big_f(sK0(X0,X1),X1)
| big_f(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1] :
( ~ big_f(X1,sK0(X0,X1))
| ~ big_f(X1,X0)
| ~ big_f(X0,X1) ),
inference(resolution,[],[f10,f14]) ).
fof(f26,plain,
! [X0] :
( ~ big_f(X0,X0)
| ~ big_f(X0,X0)
| ~ big_f(X0,sK0(X0,X0)) ),
inference(resolution,[],[f10,f13]) ).
fof(f27,plain,
! [X0] :
( ~ big_f(X0,X0)
| ~ big_f(X0,sK0(X0,X0)) ),
inference(duplicate_literal_removal,[],[f26]) ).
fof(f31,plain,
! [X0] :
( ~ big_f(sK0(X0,X0),X0)
| big_f(X0,X0)
| ~ big_f(X0,sK0(X0,X0)) ),
inference(resolution,[],[f20,f27]) ).
fof(f32,plain,
! [X0] :
( ~ big_f(sK0(X0,X0),X0)
| ~ big_f(X0,sK0(X0,X0)) ),
inference(forward_subsumption_resolution,[],[f31,f27]) ).
fof(f33,plain,
! [X0] : ~ big_f(X0,sK0(X0,X0)),
inference(forward_subsumption_resolution,[],[f32,f11]) ).
fof(f43,plain,
! [X0] : big_f(X0,X0),
inference(resolution,[],[f33,f9]) ).
fof(f52,plain,
! [X0,X1] :
( big_f(X1,X0)
| ~ big_f(X0,X1) ),
inference(resolution,[],[f43,f17]) ).
fof(f54,plain,
! [X0] :
( ~ big_f(X0,X0)
| ~ big_f(X0,X0)
| ~ big_f(sK0(X0,X0),X0) ),
inference(resolution,[],[f22,f12]) ).
fof(f61,plain,
! [X0] :
( ~ big_f(X0,X0)
| ~ big_f(sK0(X0,X0),X0) ),
inference(duplicate_literal_removal,[],[f54]) ).
fof(f64,plain,
! [X0] : ~ big_f(sK0(X0,X0),X0),
inference(forward_subsumption_resolution,[],[f61,f43]) ).
fof(f76,plain,
! [X0] :
( ~ big_f(sK0(X0,sK0(X0,X0)),sK0(X0,X0))
| big_f(X0,sK0(X0,X0)) ),
inference(resolution,[],[f64,f20]) ).
fof(f77,plain,
! [X0] : ~ big_f(sK0(X0,sK0(X0,X0)),sK0(X0,X0)),
inference(forward_subsumption_resolution,[],[f76,f33]) ).
fof(f90,plain,
! [X0] : ~ big_f(sK0(X0,X0),sK0(X0,sK0(X0,X0))),
inference(resolution,[],[f77,f52]) ).
fof(f97,plain,
! [X0] : ~ big_f(X0,sK0(X0,sK0(X0,X0))),
inference(resolution,[],[f90,f13]) ).
fof(f106,plain,
! [X0] : big_f(sK0(X0,X0),X0),
inference(resolution,[],[f97,f8]) ).
fof(f109,plain,
$false,
inference(forward_subsumption_resolution,[],[f106,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n017.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 15:38:06 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.25/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running first-order theorem proving
% 0.25/0.32 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
% 5.10/1.78 % (3655025)Detected formulas, will run a generic FOF schedule.
% 5.10/1.78 % (3655030)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=1742040562:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.10/1.78 % (3655035)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3601143367:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.10/1.78 % (3655035)First to succeed.
% 5.10/1.78 % (3655035)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3655025"
% 5.10/1.78 % (3655034)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4112765740:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.10/1.78 % (3655036)dis-21_1_sil=8000:lcm=predicate:random_seed=1220131603: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)
% 5.10/1.78 % (3655031)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=579008647:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.10/1.78 % (3655032)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=888416938:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.10/1.78 % (3655034)Also succeeded, but the first one will report.
% 5.10/1.78 % (3655036)Also succeeded, but the first one will report.
% 5.10/1.78 % (3655033)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2457224410:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.10/1.78 % (3655033)Also succeeded, but the first one will report.
% 5.10/1.78 % (3655035)Refutation found. Thanks to Tanya!
% 5.10/1.78 % SZS status Theorem for theBenchmark
% 5.10/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 5.10/1.78 % (3655035)------------------------------
% 5.10/1.78 % (3655035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.78 % (3655035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.78 % (3655035)CaDiCaL version: 2.1.3
% 5.10/1.78 % (3655035)Termination reason: Refutation
% 5.10/1.78 % (3655035)Time elapsed: 0.004 s
% 5.10/1.78 % (3655035)Peak memory usage: 89 MB
% 5.10/1.78 % (3655035)Instructions burned: 4 (million)
% 5.10/1.78 % (3655035)------------------------------
% 5.10/1.78 % (3655035)------------------------------
% 5.10/1.78 % (3655025)Success in time 0.589 s
% 5.10/1.78 % Vampire exiting
%------------------------------------------------------------------------------