%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN036+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Thu Sep 24 03:14:57 PM UTC 2026
% Result : Theorem 0.09s 0.60s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 34
% Syntax : Number of formulae : 188 ( 1 unt; 33 def)
% Number of atoms : 594 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 691 ( 285 ~; 301 |; 36 &)
% ( 66 <=>; 0 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 36 ( 35 usr; 32 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-1 aty)
% Number of variables : 194 ( 158 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
<=> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
<=> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
<~> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( sP0_prd
<~> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,definition,
! [X1,Y1] :
( sP1_prd(Y1,X1)
<=> ( big_q(X1)
<=> big_q(Y1) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f7,definition,
( sP2_prd
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f8,plain,
( sP0_prd
<~> ( ? [X1] :
! [Y1] : sP1_prd(Y1,X1)
<=> sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f5,f7,f6]) ).
fof(f9,plain,
( ( ( ( sP2_prd
| ? [X1] :
! [Y1] : sP1_prd(Y1,X1) )
& ( ~ sP2_prd
| ! [X1] :
? [Y1] : ~ sP1_prd(Y1,X1) ) )
| ~ sP0_prd )
& ( ( ( ~ sP2_prd
| ? [X1] :
! [Y1] : sP1_prd(Y1,X1) )
& ( sP2_prd
| ! [X1] :
? [Y1] : ~ sP1_prd(Y1,X1) ) )
| sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
( ( ( ( sP2_prd
| ! [Y1] : sP1_prd(Y1,sK3_skl) )
& ( ~ sP2_prd
| ! [X1] : ~ sP1_prd(sK2_skl(X1),X1) ) )
| ~ sP0_prd )
& ( ( ( ~ sP2_prd
| ! [Y1] : sP1_prd(Y1,sK1_skl) )
& ( sP2_prd
| ! [X1] : ~ sP1_prd(sK0_skl(X1),X1) ) )
| sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(Y1,sK0_skl(X1)),skolemize(X1,sK1_skl),skolemize(Y1,sK2_skl(X1)),skolemize(X1,sK3_skl)],[f9]) ).
fof(f11,plain,
! [X0] :
( sP2_prd
| ~ sP1_prd(sK0_skl(X0),X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] :
( ~ sP2_prd
| sP1_prd(X0,sK1_skl)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0] :
( ~ sP2_prd
| ~ sP1_prd(sK2_skl(X0),X0)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [X0] :
( sP2_prd
| sP1_prd(X0,sK3_skl)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f15,definition,
! [X,Y] :
( sP3_prd(Y,X)
<=> ( big_p(X)
<=> big_p(Y) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f16,definition,
( sP4_prd
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f17,plain,
( sP0_prd
<=> ( ? [X] :
! [Y] : sP3_prd(Y,X)
<=> sP4_prd ) ),
inference(formula_renaming,[status(thm)],[f4,f16,f15]) ).
fof(f18,plain,
( ( ( ( sP4_prd
| ? [X] :
! [Y] : sP3_prd(Y,X) )
& ( ~ sP4_prd
| ! [X] :
? [Y] : ~ sP3_prd(Y,X) ) )
| sP0_prd )
& ( ( ( ~ sP4_prd
| ? [X] :
! [Y] : sP3_prd(Y,X) )
& ( sP4_prd
| ! [X] :
? [Y] : ~ sP3_prd(Y,X) ) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
( ( ( ( sP4_prd
| ! [Y] : sP3_prd(Y,sK7_skl) )
& ( ~ sP4_prd
| ! [X] : ~ sP3_prd(sK6_skl(X),X) ) )
| sP0_prd )
& ( ( ( ~ sP4_prd
| ! [Y] : sP3_prd(Y,sK5_skl) )
& ( sP4_prd
| ! [X] : ~ sP3_prd(sK4_skl(X),X) ) )
| ~ sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(Y,sK4_skl(X)),skolemize(X,sK5_skl),skolemize(Y,sK6_skl(X)),skolemize(X,sK7_skl)],[f18]) ).
fof(f20,plain,
! [X0] :
( sP4_prd
| ~ sP3_prd(sK4_skl(X0),X0)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] :
( ~ sP4_prd
| sP3_prd(X0,sK5_skl)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [X0] :
( ~ sP4_prd
| ~ sP3_prd(sK6_skl(X0),X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
! [X0] :
( sP4_prd
| sP3_prd(X0,sK7_skl)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f24,plain,
! [X1,Y1] :
( ( ( ( big_q(Y1)
| big_q(X1) )
& ( ~ big_q(Y1)
| ~ big_q(X1) ) )
| sP1_prd(Y1,X1) )
& ( ( ( ~ big_q(Y1)
| big_q(X1) )
& ( big_q(Y1)
| ~ big_q(X1) ) )
| ~ sP1_prd(Y1,X1) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
( ! [X1,Y1] :
( ( ( big_q(Y1)
| big_q(X1) )
& ( ~ big_q(Y1)
| ~ big_q(X1) ) )
| sP1_prd(Y1,X1) )
& ! [X1,Y1] :
( ( ( ~ big_q(Y1)
| big_q(X1) )
& ( big_q(Y1)
| ~ big_q(X1) ) )
| ~ sP1_prd(Y1,X1) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( big_q(X0)
| ~ big_q(X1)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ~ big_q(X0)
| big_q(X1)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( ~ big_q(X0)
| ~ big_q(X1)
| sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( big_q(X0)
| big_q(X1)
| sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
( ( ( ( ! [W1] : big_q(W1)
| ? [U1] : big_p(U1) )
& ( ? [W1] : ~ big_q(W1)
| ! [U1] : ~ big_p(U1) ) )
| sP2_prd )
& ( ( ( ? [W1] : ~ big_q(W1)
| ? [U1] : big_p(U1) )
& ( ! [W1] : big_q(W1)
| ! [U1] : ~ big_p(U1) ) )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
( ( ( ( ! [W1] : big_q(W1)
| big_p(sK11_skl) )
& ( ~ big_q(sK10_skl)
| ! [U1] : ~ big_p(U1) ) )
| sP2_prd )
& ( ( ( ~ big_q(sK9_skl)
| big_p(sK8_skl) )
& ( ! [W1] : big_q(W1)
| ! [U1] : ~ big_p(U1) ) )
| ~ sP2_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl]),skolemize(U1,sK8_skl),skolemize(W1,sK9_skl),skolemize(W1,sK10_skl),skolemize(U1,sK11_skl)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( big_q(X1)
| ~ big_p(X0)
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ~ big_q(sK9_skl)
| big_p(sK8_skl)
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] :
( ~ big_q(sK10_skl)
| ~ big_p(X0)
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0] :
( big_q(X0)
| big_p(sK11_skl)
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f36,plain,
! [X,Y] :
( ( ( ( big_p(Y)
| big_p(X) )
& ( ~ big_p(Y)
| ~ big_p(X) ) )
| sP3_prd(Y,X) )
& ( ( ( ~ big_p(Y)
| big_p(X) )
& ( big_p(Y)
| ~ big_p(X) ) )
| ~ sP3_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
( ! [X,Y] :
( ( ( big_p(Y)
| big_p(X) )
& ( ~ big_p(Y)
| ~ big_p(X) ) )
| sP3_prd(Y,X) )
& ! [X,Y] :
( ( ( ~ big_p(Y)
| big_p(X) )
& ( big_p(Y)
| ~ big_p(X) ) )
| ~ sP3_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( big_p(X0)
| ~ big_p(X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ~ big_p(X0)
| big_p(X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
! [X0,X1] :
( ~ big_p(X0)
| ~ big_p(X1)
| sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( big_p(X0)
| big_p(X1)
| sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f42,plain,
( ( ( ( ! [W] : big_p(W)
| ? [U] : big_q(U) )
& ( ? [W] : ~ big_p(W)
| ! [U] : ~ big_q(U) ) )
| sP4_prd )
& ( ( ( ? [W] : ~ big_p(W)
| ? [U] : big_q(U) )
& ( ! [W] : big_p(W)
| ! [U] : ~ big_q(U) ) )
| ~ sP4_prd ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f43,plain,
( ( ( ( ! [W] : big_p(W)
| big_q(sK15_skl) )
& ( ~ big_p(sK14_skl)
| ! [U] : ~ big_q(U) ) )
| sP4_prd )
& ( ( ( ~ big_p(sK13_skl)
| big_q(sK12_skl) )
& ( ! [W] : big_p(W)
| ! [U] : ~ big_q(U) ) )
| ~ sP4_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl,sK15_skl]),skolemize(U,sK12_skl),skolemize(W,sK13_skl),skolemize(W,sK14_skl),skolemize(U,sK15_skl)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( big_p(X1)
| ~ big_q(X0)
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
( ~ big_p(sK13_skl)
| big_q(sK12_skl)
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0] :
( ~ big_p(sK14_skl)
| ~ big_q(X0)
| sP4_prd ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f47,plain,
! [X0] :
( big_p(X0)
| big_q(sK15_skl)
| sP4_prd ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f48,definition,
( sQ0_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f51,definition,
! [X0] :
( sQ1_spl
<=> ~ sP1_prd(sK0_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f52,plain,
! [X0] :
( ~ sQ1_spl
| ~ sP1_prd(sK0_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ2_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f48,f51,f54]) ).
fof(f58,definition,
! [X0] :
( sQ3_spl
<=> sP1_prd(X0,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f59,plain,
! [X0] :
( ~ sQ3_spl
| sP1_prd(X0,sK1_skl) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( ~ sQ2_spl
| sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f12,f48,f58,f54]) ).
fof(f62,definition,
! [X0] :
( sQ4_spl
<=> ~ sP1_prd(sK2_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f63,plain,
! [X0] :
( ~ sQ4_spl
| ~ sP1_prd(sK2_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,plain,
( ~ sQ2_spl
| sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f13,f48,f62,f54]) ).
fof(f66,definition,
! [X0] :
( sQ5_spl
<=> sP1_prd(X0,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f67,plain,
! [X0] :
( ~ sQ5_spl
| sP1_prd(X0,sK3_skl) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( sQ2_spl
| sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f48,f66,f54]) ).
fof(f70,definition,
! [X0] :
( sQ6_spl
<=> ~ sP3_prd(sK4_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f71,plain,
! [X0] :
( ~ sQ6_spl
| ~ sP3_prd(sK4_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ7_spl
<=> sP4_prd ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( sQ7_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f48,f70,f73]) ).
fof(f77,definition,
! [X0] :
( sQ8_spl
<=> sP3_prd(X0,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f78,plain,
! [X0] :
( ~ sQ8_spl
| sP3_prd(X0,sK5_skl) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( ~ sQ7_spl
| sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f48,f77,f73]) ).
fof(f81,definition,
! [X0] :
( sQ9_spl
<=> ~ sP3_prd(sK6_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f82,plain,
! [X0] :
( ~ sQ9_spl
| ~ sP3_prd(sK6_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( ~ sQ7_spl
| sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f22,f48,f81,f73]) ).
fof(f85,definition,
! [X0] :
( sQ10_spl
<=> sP3_prd(X0,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f86,plain,
! [X0] :
( ~ sQ10_spl
| sP3_prd(X0,sK7_skl) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ7_spl
| sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f23,f48,f85,f73]) ).
fof(f89,definition,
! [X0] :
( sQ11_spl
<=> ~ big_p(X0) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f90,plain,
! [X0] :
( ~ sQ11_spl
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,definition,
! [X1] :
( sQ12_spl
<=> big_q(X1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f93,plain,
! [X0] :
( ~ sQ12_spl
| big_q(X0) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( sQ12_spl
| sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f32,f54,f89,f92]) ).
fof(f96,definition,
( sQ13_spl
<=> big_p(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ13_spl
| big_p(sK8_skl) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
( sQ14_spl
<=> big_q(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ14_spl
| ~ big_q(sK9_skl) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( ~ sQ14_spl
| sQ13_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f33,f54,f96,f99]) ).
fof(f103,definition,
( sQ15_spl
<=> big_q(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( sQ15_spl
| ~ big_q(sK10_skl) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( ~ sQ15_spl
| sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f34,f54,f89,f103]) ).
fof(f107,definition,
( sQ16_spl
<=> big_p(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ16_spl
| big_p(sK11_skl) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ12_spl
| sQ16_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f35,f54,f107,f92]) ).
fof(f111,definition,
! [X0] :
( sQ17_spl
<=> ~ big_q(X0) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f112,plain,
! [X0] :
( ~ sQ17_spl
| ~ big_q(X0) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,definition,
! [X1] :
( sQ18_spl
<=> big_p(X1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f115,plain,
! [X0] :
( ~ sQ18_spl
| big_p(X0) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( sQ18_spl
| sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f73,f111,f114]) ).
fof(f118,definition,
( sQ19_spl
<=> big_q(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ19_spl
| big_q(sK12_skl) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ20_spl
<=> big_p(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sQ20_spl
| ~ big_p(sK13_skl) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( ~ sQ20_spl
| sQ19_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f73,f118,f121]) ).
fof(f125,definition,
( sQ21_spl
<=> big_p(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( sQ21_spl
| ~ big_p(sK14_skl) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( ~ sQ21_spl
| sQ17_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f73,f111,f125]) ).
fof(f129,definition,
( sQ22_spl
<=> big_q(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ22_spl
| big_q(sK15_skl) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ18_spl
| sQ22_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f73,f129,f114]) ).
fof(f133,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f112]) ).
fof(f134,plain,
( ~ sQ12_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f115]) ).
fof(f136,plain,
( ~ sQ11_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f130,f112]) ).
fof(f138,plain,
( ~ sQ22_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( sQ21_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f115]) ).
fof(f140,plain,
( sQ21_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f90]) ).
fof(f142,plain,
( ~ sQ16_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f141]) ).
fof(f143,plain,
( sQ15_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f93]) ).
fof(f144,plain,
( sQ15_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f143]) ).
fof(f147,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| $false ),
inference(resolution,[status(thm)],[f71,f86]) ).
fof(f148,plain,
( ~ sQ10_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f152,plain,
! [X0] :
( ~ sQ3_spl
| ~ big_q(X0)
| big_q(sK1_skl) ),
inference(resolution,[status(thm)],[f59,f27]) ).
fof(f153,plain,
! [X0] :
( ~ sQ3_spl
| big_q(X0)
| ~ big_q(sK1_skl) ),
inference(resolution,[status(thm)],[f59,f26]) ).
fof(f155,plain,
! [X0] :
( ~ sQ5_spl
| ~ big_q(X0)
| big_q(sK3_skl) ),
inference(resolution,[status(thm)],[f67,f27]) ).
fof(f156,plain,
! [X0] :
( ~ sQ5_spl
| big_q(X0)
| ~ big_q(sK3_skl) ),
inference(resolution,[status(thm)],[f67,f26]) ).
fof(f157,definition,
( sQ23_spl
<=> big_q(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ5_spl
| sQ17_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f155,f157,f111,f66]) ).
fof(f161,plain,
( ~ sQ5_spl
| sQ12_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f156,f157,f92,f66]) ).
fof(f164,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(resolution,[status(thm)],[f63,f67]) ).
fof(f165,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f166,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ big_q(X1)
| sP1_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f28,f93]) ).
fof(f167,plain,
! [X0,X1] :
( ~ sQ12_spl
| sP1_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f93]) ).
fof(f168,plain,
! [X0,X1] :
( ~ sQ11_spl
| big_p(X1)
| sP3_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f41,f90]) ).
fof(f169,plain,
! [X0,X1] :
( ~ sQ11_spl
| sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f90]) ).
fof(f170,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f52,f167]) ).
fof(f171,plain,
( ~ sQ1_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f172,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f90]) ).
fof(f173,plain,
( ~ sQ13_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
( ~ sQ19_spl
| ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f119,f112]) ).
fof(f175,plain,
( ~ sQ19_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f178,plain,
! [X0,X1] :
( big_q(X1)
| ~ big_q(X0)
| ~ big_q(X1)
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f179,definition,
! [X0] :
( sQ24_spl
<=> ( ~ big_q(X0)
| ~ big_q(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f180,plain,
! [X0] :
( ~ sQ24_spl
| ~ big_q(X0)
| ~ big_q(X0) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
! [X1] :
( sQ25_spl
<=> ( big_q(X1)
| ~ big_q(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f178,f179,f182]) ).
fof(f186,plain,
! [X0] :
( ~ sQ24_spl
| ~ big_q(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f180]) ).
fof(f188,plain,
( ~ sQ22_spl
| ~ sQ24_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f130,f186]) ).
fof(f190,plain,
( ~ sQ22_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f191,plain,
! [X0,X1] :
( ~ sQ11_spl
| big_p(X0)
| sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f90]) ).
fof(f192,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(resolution,[status(thm)],[f82,f78]) ).
fof(f193,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| big_p(sK6_skl(X0)) ),
inference(resolution,[status(thm)],[f82,f191]) ).
fof(f194,plain,
( ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f196,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f169]) ).
fof(f197,plain,
( ~ sQ6_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f202,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(resolution,[status(thm)],[f82,f86]) ).
fof(f205,plain,
( ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f209,plain,
! [X0,X1] :
( ~ sQ17_spl
| big_q(X1)
| sP1_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f29,f112]) ).
fof(f210,plain,
! [X0,X1] :
( ~ sQ17_spl
| sP1_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f112]) ).
fof(f211,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f63,f210]) ).
fof(f212,plain,
( ~ sQ4_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( sQ14_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f93]) ).
fof(f214,plain,
( sQ14_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f215,definition,
( sQ26_spl
<=> big_q(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ3_spl
| sQ17_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f152,f215,f111,f58]) ).
fof(f219,plain,
( ~ sQ3_spl
| sQ12_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f153,f215,f92,f58]) ).
fof(f230,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f167]) ).
fof(f231,plain,
( ~ sQ4_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f233,plain,
! [X0] :
( ~ sQ16_spl
| big_p(X0)
| ~ sP3_prd(sK11_skl,X0) ),
inference(resolution,[status(thm)],[f108,f39]) ).
fof(f241,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f52,f210]) ).
fof(f242,plain,
( ~ sQ1_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| big_p(sK5_skl) ),
inference(resolution,[status(thm)],[f233,f78]) ).
fof(f253,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ16_spl
| big_p(X0)
| ~ sP3_prd(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f244,f38]) ).
fof(f254,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ16_spl
| big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f78]) ).
fof(f257,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ16_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f254]) ).
fof(f259,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f260,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ big_p(X0)
| sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f115]) ).
fof(f261,plain,
! [X0,X1] :
( ~ sQ18_spl
| sP3_prd(X0,X1) ),
inference(resolution,[status(thm)],[f260,f115]) ).
fof(f262,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f71,f261]) ).
fof(f263,plain,
( ~ sQ6_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f264,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f261]) ).
fof(f265,plain,
( ~ sQ9_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f270,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f90]) ).
fof(f271,plain,
( ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f277,plain,
! [X0] :
( ~ sQ10_spl
| big_p(X0)
| ~ big_p(sK7_skl) ),
inference(resolution,[status(thm)],[f86,f38]) ).
fof(f278,plain,
! [X0] :
( ~ sQ10_spl
| ~ big_p(X0)
| big_p(sK7_skl) ),
inference(resolution,[status(thm)],[f86,f39]) ).
fof(f279,definition,
( sQ28_spl
<=> big_p(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( ~ sQ10_spl
| sQ18_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f277,f279,f114,f85]) ).
fof(f283,plain,
( ~ sQ10_spl
| sQ11_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f278,f279,f89,f85]) ).
fof(f284,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f61,f65,f69,f76,f80,f84,f88,f95,f102,f106,f110,f117,f124,f128,f132,f134,f136,f138,f140,f142,f144,f148,f160,f161,f165,f171,f173,f175,f185,f190,f194,f197,f205,f212,f214,f218,f219,f231,f242,f259,f263,f265,f271,f282,f283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN036+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n001.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 10:44:59 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 0.09/0.60 % Refutation found
% 0.09/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.62 % Elapsed time: 0.049874 seconds
% 0.09/0.62 % CPU time: 0.153282 seconds
% 0.09/0.62 % Total memory used: 9.500 MB
% 0.09/0.62 % Net memory used: 9.402 MB
%------------------------------------------------------------------------------