%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN059+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 03:15:04 PM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 9 unt; 14 def)
% Number of atoms : 282 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 316 ( 126 ~; 138 |; 28 &)
% ( 16 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 13 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 67 ( 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X] : big_f(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
? [Y] : big_g(Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
( ( ! [U] :
( big_g(U)
=> big_j(U) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
<=> ! [W,Y] :
( ( big_g(Y)
& big_f(W) )
=> ( big_j(Y)
& big_h(W) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ( ( ! [U] :
( big_g(U)
=> big_j(U) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
<=> ! [W,Y] :
( ( big_g(Y)
& big_f(W) )
=> ( big_j(Y)
& big_h(W) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
big_f(sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f1]) ).
fof(f6,plain,
big_f(sK0_skl),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
big_g(sK1_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl)],[f2]) ).
fof(f8,plain,
big_g(sK1_skl),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
( ( ! [U] :
( big_j(U)
| ~ big_g(U) )
& ! [X] :
( big_h(X)
| ~ big_f(X) ) )
<~> ! [W,Y] :
( ( big_j(Y)
& big_h(W) )
| ~ big_g(Y)
| ~ big_f(W) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f10,definition,
! [X] :
( sP0_prd(X)
<=> ( big_h(X)
| ~ big_f(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f11,definition,
! [U] :
( sP1_prd(U)
<=> ( big_j(U)
| ~ big_g(U) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f12,plain,
( ( ! [U] : sP1_prd(U)
& ! [X] : sP0_prd(X) )
<~> ! [W,Y] :
( ( big_j(Y)
& big_h(W) )
| ~ big_g(Y)
| ~ big_f(W) ) ),
inference(formula_renaming,[status(thm)],[f9,f11,f10]) ).
fof(f13,plain,
( ( ? [W,Y] :
( ( ~ big_j(Y)
| ~ big_h(W) )
& big_g(Y)
& big_f(W) )
| ? [U] : ~ sP1_prd(U)
| ? [X] : ~ sP0_prd(X) )
& ( ! [W,Y] :
( ( big_j(Y)
& big_h(W) )
| ~ big_g(Y)
| ~ big_f(W) )
| ( ! [U] : sP1_prd(U)
& ! [X] : sP0_prd(X) ) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
( ( ( ( ~ big_j(sK5_skl)
| ~ big_h(sK4_skl) )
& big_g(sK5_skl)
& big_f(sK4_skl) )
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) )
& ( ! [W,Y] :
( ( big_j(Y)
& big_h(W) )
| ~ big_g(Y)
| ~ big_f(W) )
| ( ! [U] : sP1_prd(U)
& ! [X] : sP0_prd(X) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK2_skl),skolemize(U,sK3_skl),skolemize(W,sK4_skl),skolemize(Y,sK5_skl)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( big_h(X1)
| ~ big_g(X2)
| ~ big_f(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( big_j(X2)
| ~ big_g(X2)
| ~ big_f(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
! [X0,X1,X2] :
( big_j(X2)
| ~ big_g(X2)
| ~ big_f(X1)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,plain,
( big_f(sK4_skl)
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f20,plain,
( big_g(sK5_skl)
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f21,plain,
( ~ big_j(sK5_skl)
| ~ big_h(sK4_skl)
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f22,plain,
! [X] :
( ( ( ~ big_h(X)
& big_f(X) )
| sP0_prd(X) )
& ( big_h(X)
| ~ big_f(X)
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
( ! [X] :
( ( ~ big_h(X)
& big_f(X) )
| sP0_prd(X) )
& ! [X] :
( big_h(X)
| ~ big_f(X)
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( big_h(X0)
| ~ big_f(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] :
( big_f(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0] :
( ~ big_h(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,plain,
! [U] :
( ( ( ~ big_j(U)
& big_g(U) )
| sP1_prd(U) )
& ( big_j(U)
| ~ big_g(U)
| ~ sP1_prd(U) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
( ! [U] :
( ( ~ big_j(U)
& big_g(U) )
| sP1_prd(U) )
& ! [U] :
( big_j(U)
| ~ big_g(U)
| ~ sP1_prd(U) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0] :
( big_j(X0)
| ~ big_g(X0)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0] :
( big_g(X0)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0] :
( ~ big_j(X0)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f33,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,definition,
! [X1] :
( sQ1_spl
<=> ( big_h(X1)
| ~ big_f(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f36,plain,
! [X0] :
( ~ sQ1_spl
| big_h(X0)
| ~ big_f(X0) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
! [X2] :
( sQ2_spl
<=> ~ big_g(X2) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f39,plain,
! [X0] :
( ~ sQ2_spl
| ~ big_g(X0) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f32,f35,f38]) ).
fof(f42,definition,
! [X1] :
( sQ3_spl
<=> ~ big_f(X1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f43,plain,
! [X0] :
( ~ sQ3_spl
| ~ big_f(X0) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
! [X2] :
( sQ4_spl
<=> ( big_j(X2)
| ~ big_g(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f46,plain,
! [X0] :
( ~ sQ4_spl
| big_j(X0)
| ~ big_g(X0) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ4_spl
| sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f32,f42,f45]) ).
fof(f49,definition,
! [X0] :
( sQ5_spl
<=> sP1_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f50,plain,
! [X0] :
( ~ sQ5_spl
| sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f53,plain,
( sQ4_spl
| sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f18,f49,f42,f45]) ).
fof(f54,definition,
( sQ6_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ6_spl
| ~ sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ7_spl
<=> sP1_prd(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ7_spl
| ~ sP1_prd(sK3_skl) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ8_spl
<=> big_f(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ8_spl
| big_f(sK4_skl) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f19,f54,f57,f60]) ).
fof(f64,definition,
( sQ9_spl
<=> big_g(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ9_spl
| big_g(sK5_skl) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f20,f54,f57,f64]) ).
fof(f68,definition,
( sQ10_spl
<=> big_h(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( sQ10_spl
| ~ big_h(sK4_skl) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,definition,
( sQ11_spl
<=> big_j(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( sQ11_spl
| ~ big_j(sK5_skl) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f21,f54,f57,f68,f71]) ).
fof(f75,plain,
( sQ7_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f50]) ).
fof(f76,plain,
( sQ7_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f77,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6,f43]) ).
fof(f78,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f79,plain,
( sQ6_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f56,f33]) ).
fof(f80,plain,
( sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( sQ7_spl
| ~ big_j(sK3_skl) ),
inference(resolution,[status(thm)],[f59,f31]) ).
fof(f83,plain,
( sQ7_spl
| big_g(sK3_skl) ),
inference(resolution,[status(thm)],[f30,f59]) ).
fof(f84,plain,
( ~ sQ4_spl
| sQ7_spl
| big_j(sK3_skl) ),
inference(resolution,[status(thm)],[f83,f46]) ).
fof(f85,plain,
( ~ sQ4_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f81]) ).
fof(f86,plain,
( ~ sQ4_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0] :
( ~ sQ0_spl
| big_h(X0)
| ~ big_f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f33]) ).
fof(f88,plain,
( sQ10_spl
| ~ sQ0_spl
| ~ big_f(sK4_skl) ),
inference(resolution,[status(thm)],[f87,f70]) ).
fof(f89,plain,
( sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f61]) ).
fof(f90,plain,
( sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f91,plain,
( sQ6_spl
| ~ big_h(sK2_skl) ),
inference(resolution,[status(thm)],[f26,f56]) ).
fof(f92,plain,
( ~ sQ1_spl
| sQ6_spl
| ~ big_f(sK2_skl) ),
inference(resolution,[status(thm)],[f91,f36]) ).
fof(f93,plain,
( ~ sQ1_spl
| sQ6_spl
| sP0_prd(sK2_skl) ),
inference(resolution,[status(thm)],[f92,f25]) ).
fof(f94,plain,
( ~ sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f93,f54,f35]) ).
fof(f96,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f8,f39]) ).
fof(f97,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f98,plain,
( sQ11_spl
| ~ sQ4_spl
| ~ big_g(sK5_skl) ),
inference(resolution,[status(thm)],[f46,f73]) ).
fof(f99,plain,
( sQ11_spl
| ~ sQ4_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f65]) ).
fof(f100,plain,
( sQ11_spl
| ~ sQ4_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ sQ5_spl
| big_j(X0)
| ~ big_g(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f50]) ).
fof(f102,plain,
( sQ11_spl
| ~ sQ5_spl
| ~ big_g(sK5_skl) ),
inference(resolution,[status(thm)],[f101,f73]) ).
fof(f103,plain,
( sQ11_spl
| ~ sQ5_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f65]) ).
fof(f104,plain,
( sQ11_spl
| ~ sQ5_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f103]) ).
fof(f105,plain,
( sQ10_spl
| ~ sQ1_spl
| ~ big_f(sK4_skl) ),
inference(resolution,[status(thm)],[f36,f70]) ).
fof(f106,plain,
( sQ10_spl
| ~ sQ1_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f61]) ).
fof(f107,plain,
( sQ10_spl
| ~ sQ1_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f108,plain,
$false,
inference(sat_refutation,[status(thm)],[f41,f48,f53,f63,f67,f74,f76,f78,f80,f86,f90,f94,f97,f100,f104,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN059+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 10:42:48 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.047099 seconds
% 0.14/0.41 % CPU time: 0.118832 seconds
% 0.14/0.41 % Total memory used: 16.849 MB
% 0.14/0.41 % Net memory used: 16.441 MB
%------------------------------------------------------------------------------