%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN347+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 : n026.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 01:50:18 PM UTC 2026
% Result : Theorem 2.50s 1.11s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 5 unt; 5 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 174 ( 70 ~; 74 |; 16 &)
% ( 12 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 45 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2,X3] :
! [X4] :
( ( ( big_f(X2,X4)
<=> big_f(X3,X4) )
<=> big_f(X0,X1) )
| ( big_f(X0,X4)
<=> big_f(X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_17_3) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2,X3] :
! [X4] :
( ( ( big_f(X2,X4)
<=> big_f(X3,X4) )
<=> big_f(X0,X1) )
| ( big_f(X0,X4)
<=> big_f(X1,X4) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ( big_f(X2,X4)
<=> big_f(X3,X4) )
<~> big_f(X0,X1) )
& ( big_f(X0,X4)
<~> big_f(X1,X4) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ~ big_f(X0,X1)
| ( ( ~ big_f(X3,X4)
| ~ big_f(X2,X4) )
& ( big_f(X3,X4)
| big_f(X2,X4) ) ) )
& ( big_f(X0,X1)
| ( ( big_f(X2,X4)
| ~ big_f(X3,X4) )
& ( big_f(X3,X4)
| ~ big_f(X2,X4) ) ) )
& ( ~ big_f(X1,X4)
| ~ big_f(X0,X4) )
& ( big_f(X1,X4)
| big_f(X0,X4) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ~ big_f(X0,X1)
| ( ( ~ big_f(X3,X4)
| ~ big_f(X2,X4) )
& ( big_f(X3,X4)
| big_f(X2,X4) ) ) )
& ( big_f(X0,X1)
| ( ( big_f(X2,X4)
| ~ big_f(X3,X4) )
& ( big_f(X3,X4)
| ~ big_f(X2,X4) ) ) )
& ( ~ big_f(X1,X4)
| ~ big_f(X0,X4) )
& ( big_f(X1,X4)
| big_f(X0,X4) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X2,X3] :
( ( ~ big_f(sK0,sK1)
| ( ( ~ big_f(X3,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3)) )
& ( big_f(X3,sK2(X2,X3))
| big_f(X2,sK2(X2,X3)) ) ) )
& ( big_f(sK0,sK1)
| ( ( big_f(X2,sK2(X2,X3))
| ~ big_f(X3,sK2(X2,X3)) )
& ( big_f(X3,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3)) ) ) )
& ( ~ big_f(sK1,sK2(X2,X3))
| ~ big_f(sK0,sK2(X2,X3)) )
& ( big_f(sK1,sK2(X2,X3))
| big_f(sK0,sK2(X2,X3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X2,X3))],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( big_f(sK1,sK2(X2,X3))
| big_f(sK0,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X2,X3] :
( ~ big_f(sK1,sK2(X2,X3))
| ~ big_f(sK0,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X2,X3] :
( big_f(sK0,sK1)
| big_f(X3,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X3] :
( big_f(sK0,sK1)
| big_f(X2,sK2(X2,X3))
| ~ big_f(X3,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
! [X2,X3] :
( ~ big_f(sK0,sK1)
| big_f(X3,sK2(X2,X3))
| big_f(X2,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
! [X2,X3] :
( ~ big_f(sK0,sK1)
| ~ big_f(X3,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,definition,
( spl3_1
<=> ! [X2,X3] :
( big_f(X3,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f15,plain,
( ! [X2,X3] :
( ~ big_f(X2,sK2(X2,X3))
| big_f(X3,sK2(X2,X3)) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f17,definition,
( spl3_2
<=> big_f(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f20,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f9,f17,f14]) ).
fof(f22,definition,
( spl3_3
<=> ! [X2,X3] :
( big_f(X2,sK2(X2,X3))
| ~ big_f(X3,sK2(X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f23,plain,
( ! [X2,X3] :
( ~ big_f(X3,sK2(X2,X3))
| big_f(X2,sK2(X2,X3)) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f24,plain,
( spl3_3
| spl3_2 ),
inference(avatar_split_clause,[],[f10,f17,f22]) ).
fof(f26,definition,
( spl3_4
<=> ! [X2,X3] :
( big_f(X3,sK2(X2,X3))
| big_f(X2,sK2(X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f27,plain,
( ! [X2,X3] :
( big_f(X3,sK2(X2,X3))
| big_f(X2,sK2(X2,X3)) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f28,plain,
( spl3_4
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f11,f17,f26]) ).
fof(f30,definition,
( spl3_5
<=> ! [X2,X3] :
( ~ big_f(X3,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f31,plain,
( ! [X2,X3] :
( ~ big_f(X3,sK2(X2,X3))
| ~ big_f(X2,sK2(X2,X3)) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f32,plain,
( spl3_5
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f12,f17,f30]) ).
fof(f35,plain,
( ! [X0] : big_f(X0,sK2(X0,X0))
| ~ spl3_4 ),
inference(factoring,[],[f27]) ).
fof(f39,plain,
( ! [X0] : ~ big_f(X0,sK2(X0,X0))
| ~ spl3_4
| ~ spl3_5 ),
inference(resolution,[],[f31,f35]) ).
fof(f40,plain,
( $false
| ~ spl3_4
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f39,f35]) ).
fof(f41,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f40]) ).
fof(f48,plain,
( ! [X0] :
( big_f(sK0,sK2(sK1,X0))
| big_f(X0,sK2(sK1,X0)) )
| ~ spl3_1 ),
inference(resolution,[],[f15,f7]) ).
fof(f51,plain,
( big_f(sK0,sK2(sK1,sK0))
| ~ spl3_1 ),
inference(factoring,[],[f48]) ).
fof(f54,plain,
( big_f(sK1,sK2(sK1,sK0))
| ~ spl3_1
| ~ spl3_3 ),
inference(resolution,[],[f51,f23]) ).
fof(f56,plain,
( ~ big_f(sK0,sK2(sK1,sK0))
| ~ spl3_1
| ~ spl3_3 ),
inference(resolution,[],[f54,f8]) ).
fof(f58,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f56,f51]) ).
fof(f59,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f58]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s2,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f24]) ).
cnf(s3,plain,
( ~ spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
( ~ spl3_2
| spl3_5 ),
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(sat_conversion,[],[f41]) ).
cnf(s7,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f59]) ).
cnf(s8,plain,
~ spl3_2,
inference(rat,[],[s5,s3,s4]) ).
cnf(s9,plain,
spl3_3,
inference(rat,[],[s2,s8]) ).
cnf(s10,plain,
spl3_1,
inference(rat,[],[s1,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s7,s9,s10]) ).
fof(f60,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN347+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n026.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 15:49:12 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running first-order theorem proving
% 0.06/0.20 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
% 2.50/1.11 % (3969345)Detected formulas, will run a generic FOF schedule.
% 2.50/1.11 % (3969353)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2348905777:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.11 % (3969353)First to succeed.
% 2.50/1.11 % (3969353)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3969345"
% 2.50/1.11 % (3969355)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3017271013:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.11 % (3969356)dis-21_1_sil=8000:lcm=predicate:random_seed=4197920594: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)
% 2.50/1.11 % (3969350)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=4043817175:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.11 % (3969352)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=353548358:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.11 % (3969351)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=2903817582:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.11 % (3969355)Also succeeded, but the first one will report.
% 2.50/1.11 % (3969356)Also succeeded, but the first one will report.
% 2.50/1.11 % (3969354)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2589304772:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.11 % (3969354)Also succeeded, but the first one will report.
% 2.50/1.11 % (3969353)Refutation found. Thanks to Tanya!
% 2.50/1.11 % SZS status Theorem for theBenchmark
% 2.50/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.12 % (3969353)------------------------------
% 2.50/1.12 % (3969353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.12 % (3969353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.12 % (3969353)CaDiCaL version: 2.1.3
% 2.50/1.12 % (3969353)Termination reason: Refutation
% 2.50/1.12 % (3969353)Time elapsed: 0.002 s
% 2.50/1.12 % (3969353)Peak memory usage: 89 MB
% 2.50/1.12 % (3969353)Instructions burned: 2 (million)
% 2.50/1.12 % (3969353)------------------------------
% 2.50/1.12 % (3969353)------------------------------
% 2.50/1.12 % (3969345)Success in time 0.268 s
% 2.50/1.12 % Vampire exiting
%------------------------------------------------------------------------------