%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN036+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 185 ( 1 unt; 29 def)
% Number of atoms : 605 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 718 ( 298 ~; 319 |; 36 &)
% ( 62 <=>; 0 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 32 ( 31 usr; 28 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_q(W) ) )
<=> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(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_q(W) ) )
<=> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
<~> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(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_q(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_p(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_p(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_q(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_p(W1)
| ? [U1] : big_p(U1) )
& ( ? [W1] : ~ big_p(W1)
| ! [U1] : ~ big_p(U1) ) )
| sP2_prd )
& ( ( ( ? [W1] : ~ big_p(W1)
| ? [U1] : big_p(U1) )
& ( ! [W1] : big_p(W1)
| ! [U1] : ~ big_p(U1) ) )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
( ( ( ( ! [W1] : big_p(W1)
| big_p(sK11_skl) )
& ( ~ big_p(sK10_skl)
| ! [U1] : ~ big_p(U1) ) )
| sP2_prd )
& ( ( ( ~ big_p(sK9_skl)
| big_p(sK8_skl) )
& ( ! [W1] : big_p(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_p(X1)
| ~ big_p(X0)
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] :
( ~ big_p(sK10_skl)
| ~ big_p(X0)
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0] :
( big_p(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_q(W)
| ? [U] : big_q(U) )
& ( ? [W] : ~ big_q(W)
| ! [U] : ~ big_q(U) ) )
| sP4_prd )
& ( ( ( ? [W] : ~ big_q(W)
| ? [U] : big_q(U) )
& ( ! [W] : big_q(W)
| ! [U] : ~ big_q(U) ) )
| ~ sP4_prd ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f43,plain,
( ( ( ( ! [W] : big_q(W)
| big_q(sK15_skl) )
& ( ~ big_q(sK14_skl)
| ! [U] : ~ big_q(U) ) )
| sP4_prd )
& ( ( ( ~ big_q(sK13_skl)
| big_q(sK12_skl) )
& ( ! [W] : big_q(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_q(X1)
| ~ big_q(X0)
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
( ~ big_q(sK13_skl)
| big_q(sK12_skl)
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0] :
( ~ big_q(sK14_skl)
| ~ big_q(X0)
| sP4_prd ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f47,plain,
! [X0] :
( big_q(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_p(X1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f93,plain,
! [X0] :
( ~ sQ12_spl
| big_p(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(f103,definition,
( sQ15_spl
<=> big_p(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( sQ15_spl
| ~ big_p(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_q(X1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f115,plain,
! [X0] :
( ~ sQ18_spl
| big_q(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_q(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sQ20_spl
| ~ big_q(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_q(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ21_spl
| big_q(sK14_skl) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f127,plain,
( sQ21_spl
| ~ big_q(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,
( ~ sQ17_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f115]) ).
fof(f134,plain,
( ~ sQ17_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f93]) ).
fof(f136,plain,
( ~ sQ11_spl
| ~ sQ12_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(f145,plain,
! [X0] :
( ~ sQ22_spl
| ~ big_q(X0)
| sP1_prd(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f28,f130]) ).
fof(f146,plain,
! [X0] :
( ~ sQ5_spl
| ~ big_q(X0)
| big_q(sK3_skl) ),
inference(resolution,[status(thm)],[f67,f27]) ).
fof(f147,definition,
( sQ23_spl
<=> big_q(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ23_spl
| big_q(sK3_skl) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( ~ sQ5_spl
| sQ17_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f146,f147,f111,f66]) ).
fof(f152,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(resolution,[status(thm)],[f82,f86]) ).
fof(f153,plain,
( ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f158,plain,
( ~ sQ19_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f112]) ).
fof(f159,plain,
( ~ sQ19_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f160,plain,
! [X0,X1] :
( ~ sQ11_spl
| big_p(X1)
| sP3_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f41,f90]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sQ11_spl
| sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f160,f90]) ).
fof(f167,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f52,f67]) ).
fof(f169,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f170,plain,
! [X0,X1] :
( ~ sQ17_spl
| big_q(X1)
| sP1_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f29,f112]) ).
fof(f171,plain,
! [X0,X1] :
( ~ sQ17_spl
| sP1_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f112]) ).
fof(f172,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f52,f171]) ).
fof(f173,plain,
( ~ sQ1_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f176,plain,
! [X0] :
( sQ21_spl
| ~ big_q(X0)
| ~ sP1_prd(sK14_skl,X0) ),
inference(resolution,[status(thm)],[f127,f26]) ).
fof(f178,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f161]) ).
fof(f179,plain,
( ~ sQ6_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f182,plain,
! [X0] :
( ~ sQ1_spl
| ~ big_q(sK0_skl(X0))
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[f52,f28]) ).
fof(f183,plain,
( ~ sQ1_spl
| ~ sQ22_spl
| ~ big_q(sK0_skl(sK15_skl)) ),
inference(resolution,[status(thm)],[f145,f52]) ).
fof(f185,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ22_spl
| big_q(X0)
| sP1_prd(X0,sK0_skl(sK15_skl)) ),
inference(resolution,[status(thm)],[f183,f29]) ).
fof(f187,plain,
( ~ sQ1_spl
| ~ sQ22_spl
| sQ21_spl
| big_q(sK14_skl)
| ~ big_q(sK0_skl(sK15_skl)) ),
inference(resolution,[status(thm)],[f176,f185]) ).
fof(f191,definition,
( sQ24_spl
<=> big_q(sK0_skl(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ1_spl
| ~ sQ22_spl
| sQ21_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f187,f191,f125,f129,f51]) ).
fof(f203,plain,
! [X0,X1] :
( ~ sQ1_spl
| big_q(X1)
| sP1_prd(X1,sK0_skl(X0))
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[f182,f29]) ).
fof(f204,plain,
! [X0] :
( sQ21_spl
| ~ sQ1_spl
| ~ big_q(sK0_skl(X0))
| big_q(sK14_skl)
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[f203,f176]) ).
fof(f206,definition,
! [X0] :
( sQ26_spl
<=> ( ~ big_q(sK0_skl(X0))
| ~ big_q(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ1_spl
| sQ21_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f204,f206,f125,f51]) ).
fof(f224,plain,
! [X0] :
( sQ15_spl
| ~ big_p(X0)
| ~ sP3_prd(sK10_skl,X0) ),
inference(resolution,[status(thm)],[f38,f105]) ).
fof(f225,plain,
( ~ sQ10_spl
| sQ15_spl
| ~ big_p(sK7_skl) ),
inference(resolution,[status(thm)],[f224,f86]) ).
fof(f231,plain,
! [X0] :
( ~ sQ10_spl
| sQ15_spl
| ~ big_p(X0)
| ~ sP3_prd(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f225,f39]) ).
fof(f233,plain,
! [X0] :
( ~ sQ10_spl
| sQ15_spl
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f86]) ).
fof(f236,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f108,f233]) ).
fof(f238,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f240,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ big_q(sK3_skl) ),
inference(resolution,[status(thm)],[f67,f176]) ).
fof(f241,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f148]) ).
fof(f242,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f241]) ).
fof(f247,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f112]) ).
fof(f248,plain,
( ~ sQ21_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f252,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ big_p(X1)
| sP3_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f40,f93]) ).
fof(f254,plain,
! [X0,X1] :
( ~ sQ12_spl
| sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f93]) ).
fof(f262,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f161]) ).
fof(f263,plain,
( ~ sQ9_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f264,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f254]) ).
fof(f265,plain,
( ~ sQ9_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f266,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f171]) ).
fof(f267,plain,
( ~ sQ4_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f270,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f254]) ).
fof(f271,plain,
( ~ sQ6_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f275,plain,
( sQ20_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f115]) ).
fof(f276,plain,
( sQ20_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f275]) ).
fof(f283,plain,
( ~ sQ8_spl
| sQ15_spl
| ~ big_p(sK5_skl) ),
inference(resolution,[status(thm)],[f224,f78]) ).
fof(f289,plain,
! [X0] :
( ~ sQ8_spl
| sQ15_spl
| ~ big_p(X0)
| ~ sP3_prd(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f283,f39]) ).
fof(f291,plain,
! [X0] :
( ~ sQ8_spl
| sQ15_spl
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f289,f78]) ).
fof(f294,plain,
( ~ sQ16_spl
| ~ sQ8_spl
| sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f108,f291]) ).
fof(f296,plain,
( ~ sQ16_spl
| ~ sQ8_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f297,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ big_q(X0)
| sP1_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f28,f115]) ).
fof(f298,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ1_spl
| ~ big_q(sK0_skl(X0)) ),
inference(resolution,[status(thm)],[f52,f297]) ).
fof(f299,plain,
( ~ sQ18_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f115]) ).
fof(f300,plain,
( ~ sQ18_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f306,plain,
( ~ sQ3_spl
| sQ21_spl
| ~ big_q(sK1_skl) ),
inference(resolution,[status(thm)],[f176,f59]) ).
fof(f307,plain,
! [X0] :
( ~ sQ3_spl
| sQ21_spl
| ~ big_q(X0)
| ~ sP1_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f306,f27]) ).
fof(f308,plain,
! [X0] :
( ~ sQ3_spl
| sQ21_spl
| ~ big_q(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f59]) ).
fof(f309,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| sQ21_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f130,f308]) ).
fof(f310,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f311,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ big_q(X0)
| sP1_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f28,f115]) ).
fof(f312,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ4_spl
| ~ big_q(sK2_skl(X0)) ),
inference(resolution,[status(thm)],[f63,f311]) ).
fof(f313,plain,
( ~ sQ18_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f115]) ).
fof(f314,plain,
( ~ sQ18_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f315,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f61,f65,f69,f76,f80,f84,f88,f95,f106,f110,f117,f124,f128,f132,f134,f136,f138,f140,f142,f144,f150,f153,f159,f169,f173,f179,f194,f209,f238,f242,f248,f263,f265,f267,f271,f276,f296,f300,f310,f314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN036+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 10:39:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.38 % Refutation found
% 0.15/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.048628 seconds
% 0.15/0.43 % CPU time: 0.070969 seconds
% 0.15/0.43 % Total memory used: 4.554 MB
% 0.15/0.43 % Net memory used: 4.528 MB
%------------------------------------------------------------------------------