%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN354+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 : n019.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 01:50:20 PM UTC 2026
% Result : Theorem 2.60s 1.08s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 8 unt; 3 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 191 ( 71 ~; 67 |; 30 &)
% ( 9 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 32 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X1)
=> ( big_g(X0,X1)
=> ( ( ( big_g(X1,X4)
<=> big_g(X3,X4) )
=> ( big_f(X2,X3)
=> big_f(X1,X3) ) )
=> ( ( big_g(X1,X4)
<=> big_g(X2,X4) )
=> ( big_f(X0,X2)
& big_f(X1,X2)
& big_f(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_20_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2,X3] :
! [X4] :
( big_f(X0,X1)
=> ( big_g(X0,X1)
=> ( ( ( big_g(X1,X4)
<=> big_g(X3,X4) )
=> ( big_f(X2,X3)
=> big_f(X1,X3) ) )
=> ( ( big_g(X1,X4)
<=> big_g(X2,X4) )
=> ( big_f(X0,X2)
& big_f(X1,X2)
& big_f(X2,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ~ big_f(X0,X2)
| ~ big_f(X1,X2)
| ~ big_f(X2,X3) )
& ( big_g(X1,X4)
<=> big_g(X2,X4) )
& ( big_f(X1,X3)
| ~ big_f(X2,X3)
| ( big_g(X1,X4)
<~> big_g(X3,X4) ) )
& big_g(X0,X1)
& big_f(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ~ big_f(X0,X2)
| ~ big_f(X1,X2)
| ~ big_f(X2,X3) )
& ( big_g(X1,X4)
<=> big_g(X2,X4) )
& ( big_f(X1,X3)
| ~ big_f(X2,X3)
| ( big_g(X1,X4)
<~> big_g(X3,X4) ) )
& big_g(X0,X1)
& big_f(X0,X1) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ~ big_f(X0,X2)
| ~ big_f(X1,X2)
| ~ big_f(X2,X3) )
& ( big_g(X1,X4)
| ~ big_g(X2,X4) )
& ( big_g(X2,X4)
| ~ big_g(X1,X4) )
& ( big_f(X1,X3)
| ~ big_f(X2,X3)
| ( ( ~ big_g(X3,X4)
| ~ big_g(X1,X4) )
& ( big_g(X3,X4)
| big_g(X1,X4) ) ) )
& big_g(X0,X1)
& big_f(X0,X1) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1] :
! [X2,X3] :
? [X4] :
( ( ~ big_f(X0,X2)
| ~ big_f(X1,X2)
| ~ big_f(X2,X3) )
& ( big_g(X1,X4)
| ~ big_g(X2,X4) )
& ( big_g(X2,X4)
| ~ big_g(X1,X4) )
& ( big_f(X1,X3)
| ~ big_f(X2,X3)
| ( ( ~ big_g(X3,X4)
| ~ big_g(X1,X4) )
& ( big_g(X3,X4)
| big_g(X1,X4) ) ) )
& big_g(X0,X1)
& big_f(X0,X1) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( ( ~ big_f(sK0,X2)
| ~ big_f(sK1,X2)
| ~ big_f(X2,X3) )
& ( big_g(sK1,sK2(X2,X3))
| ~ big_g(X2,sK2(X2,X3)) )
& ( big_g(X2,sK2(X2,X3))
| ~ big_g(sK1,sK2(X2,X3)) )
& ( big_f(sK1,X3)
| ~ big_f(X2,X3)
| ( ( ~ big_g(X3,sK2(X2,X3))
| ~ big_g(sK1,sK2(X2,X3)) )
& ( big_g(X3,sK2(X2,X3))
| big_g(sK1,sK2(X2,X3)) ) ) )
& big_g(sK0,sK1)
& big_f(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X2,X3))],[f6]) ).
fof(f8,plain,
big_f(sK0,sK1),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X2,X3] :
( big_g(sK1,sK2(X2,X3))
| ~ big_f(X2,X3)
| big_g(X3,sK2(X2,X3))
| big_f(sK1,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2,X3] :
( ~ big_g(sK1,sK2(X2,X3))
| ~ big_f(X2,X3)
| ~ big_g(X3,sK2(X2,X3))
| big_f(sK1,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X2,X3] :
( ~ big_f(sK1,X2)
| ~ big_f(sK0,X2)
| ~ big_f(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0] :
( big_g(sK1,sK2(X0,sK1))
| ~ big_f(X0,sK1)
| big_f(sK1,sK1) ),
inference(factoring,[],[f10]) ).
fof(f19,definition,
( spl3_1
<=> big_f(sK1,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f21,plain,
( big_f(sK1,sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f23,definition,
( spl3_2
<=> ! [X0] :
( big_g(sK1,sK2(X0,sK1))
| ~ big_f(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f24,plain,
( ! [X0] :
( big_g(sK1,sK2(X0,sK1))
| ~ big_f(X0,sK1) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f25,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f17,f23,f19]) ).
fof(f28,plain,
( ! [X0] :
( ~ big_f(X0,sK1)
| ~ big_f(X0,sK1)
| ~ big_g(sK1,sK2(X0,sK1))
| big_f(sK1,sK1) )
| ~ spl3_2 ),
inference(resolution,[],[f24,f11]) ).
fof(f31,plain,
( ! [X0] :
( ~ big_f(X0,sK1)
| ~ big_g(sK1,sK2(X0,sK1))
| big_f(sK1,sK1) )
| ~ spl3_2 ),
inference(duplicate_literal_removal,[],[f28]) ).
fof(f32,plain,
( ! [X0] :
( ~ big_f(X0,sK1)
| big_f(sK1,sK1) )
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f31,f24]) ).
fof(f34,definition,
( spl3_3
<=> ! [X0] : ~ big_f(X0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f35,plain,
( ! [X0] : ~ big_f(X0,sK1)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( spl3_1
| spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f32,f23,f34,f19]) ).
fof(f37,plain,
( ! [X0] :
( ~ big_f(sK0,sK1)
| ~ big_f(sK1,X0) )
| ~ spl3_1 ),
inference(resolution,[],[f21,f14]) ).
fof(f38,plain,
( ! [X0] : ~ big_f(sK1,X0)
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f37,f8]) ).
fof(f39,plain,
( $false
| ~ spl3_1 ),
inference(resolution,[],[f38,f21]) ).
fof(f40,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f39]) ).
fof(f41,plain,
( $false
| ~ spl3_3 ),
inference(resolution,[],[f35,f8]) ).
fof(f42,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f41]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
( spl3_1
| ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f36]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
~ spl3_3,
inference(sat_conversion,[],[f42]) ).
cnf(s5,plain,
~ spl3_2,
inference(rat,[],[s2,s4,s3]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s3]) ).
fof(f43,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN354+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.19 % Computer : n019.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Mon Sep 28 15:47:48 UTC 2026
% 0.13/0.20 % CPUTime :
% 0.13/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.22 Running first-order theorem proving
% 0.13/0.22 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
% 2.60/1.08 % (4112098)Detected formulas, will run a generic FOF schedule.
% 2.60/1.08 % (4112153)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3117937822:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.08 % (4112153)First to succeed.
% 2.60/1.08 % (4112153)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4112098"
% 2.60/1.08 % (4112155)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1057404306:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.08 % (4112150)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=1955820939:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.08 % (4112157)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2553087128:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.08 % (4112152)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=3054652243:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.08 % (4112155)Also succeeded, but the first one will report.
% 2.60/1.08 % (4112157)Also succeeded, but the first one will report.
% 2.60/1.08 % (4112158)dis-21_1_sil=8000:lcm=predicate:random_seed=2416944413: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)
% 2.60/1.08 % (4112158)Also succeeded, but the first one will report.
% 2.60/1.08 % (4112149)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=1496935422:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.08 % (4112153)Refutation found. Thanks to Tanya!
% 2.60/1.08 % SZS status Theorem for theBenchmark
% 2.60/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.08 % (4112153)------------------------------
% 2.60/1.08 % (4112153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.08 % (4112153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.08 % (4112153)CaDiCaL version: 2.1.3
% 2.60/1.08 % (4112153)Termination reason: Refutation
% 2.60/1.08 % (4112153)Time elapsed: 0.002 s
% 2.60/1.08 % (4112153)Peak memory usage: 89 MB
% 2.60/1.08 % (4112153)Instructions burned: 2 (million)
% 2.60/1.08 % (4112153)------------------------------
% 2.60/1.08 % (4112153)------------------------------
% 2.60/1.08 % (4112098)Success in time 0.284 s
% 2.60/1.08 % Vampire exiting
%------------------------------------------------------------------------------