%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN056+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 : n007.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 03:15:03 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 1 unt; 12 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 245 ( 110 ~; 102 |; 10 &)
% ( 17 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 13 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 49 ( 43 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ? [X] : big_p(X)
<=> ? [Y] : big_q(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( ( big_q(Y)
& big_p(X) )
=> ( big_r(X)
<=> big_s(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
( ! [X] :
( big_p(X)
=> big_r(X) )
<=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ( ! [X] :
( big_p(X)
=> big_r(X) )
<=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
( ( ! [Y] : ~ big_q(Y)
| ? [X] : big_p(X) )
& ( ? [Y] : big_q(Y)
| ! [X] : ~ big_p(X) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
( ( ! [Y] : ~ big_q(Y)
| big_p(sK1_skl) )
& ( big_q(sK0_skl)
| ! [X] : ~ big_p(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f5]) ).
fof(f7,plain,
! [X0] :
( big_q(sK0_skl)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ big_q(X0)
| big_p(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X,Y] :
( ( big_r(X)
<=> big_s(Y) )
| ~ big_q(Y)
| ~ big_p(X) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X,Y] :
( ( ( ~ big_s(Y)
| big_r(X) )
& ( big_s(Y)
| ~ big_r(X) ) )
| ~ big_q(Y)
| ~ big_p(X) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( big_s(X1)
| ~ big_r(X0)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ~ big_s(X1)
| big_r(X0)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
( ! [X] :
( big_r(X)
| ~ big_p(X) )
<~> ! [Y] :
( big_s(Y)
| ~ big_q(Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
( ( ? [Y] :
( ~ big_s(Y)
& big_q(Y) )
| ? [X] :
( ~ big_r(X)
& big_p(X) ) )
& ( ! [Y] :
( big_s(Y)
| ~ big_q(Y) )
| ! [X] :
( big_r(X)
| ~ big_p(X) ) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ( ( ~ big_s(sK3_skl)
& big_q(sK3_skl) )
| ( ~ big_r(sK2_skl)
& big_p(sK2_skl) ) )
& ( ! [Y] :
( big_s(Y)
| ~ big_q(Y) )
| ! [X] :
( big_r(X)
| ~ big_p(X) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( big_s(X1)
| ~ big_q(X1)
| big_r(X0)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( big_q(sK3_skl)
| big_p(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
( ~ big_s(sK3_skl)
| big_p(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
( big_q(sK3_skl)
| ~ big_r(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f20,plain,
( ~ big_s(sK3_skl)
| ~ big_r(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f21,definition,
! [X0] :
( sQ0_spl
<=> ~ big_p(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ0_spl
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,definition,
( sQ1_spl
<=> big_q(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f25,plain,
( ~ sQ1_spl
| big_q(sK0_skl) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f21,f24]) ).
fof(f28,definition,
( sQ2_spl
<=> big_p(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f29,plain,
( ~ sQ2_spl
| big_p(sK1_skl) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,definition,
! [X0] :
( sQ3_spl
<=> ~ big_q(X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f32,plain,
! [X0] :
( ~ sQ3_spl
| ~ big_q(X0) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f8,f28,f31]) ).
fof(f35,definition,
! [X0] :
( sQ4_spl
<=> ( ~ big_r(X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f36,plain,
! [X0] :
( ~ sQ4_spl
| ~ big_r(X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
! [X1] :
( sQ5_spl
<=> ( big_s(X1)
| ~ big_q(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f39,plain,
! [X0] :
( ~ sQ5_spl
| big_s(X0)
| ~ big_q(X0) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f11,f35,f38]) ).
fof(f42,definition,
! [X0] :
( sQ6_spl
<=> ( big_r(X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f43,plain,
! [X0] :
( ~ sQ6_spl
| big_r(X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
! [X1] :
( sQ7_spl
<=> ( ~ big_s(X1)
| ~ big_q(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f46,plain,
! [X0] :
( ~ sQ7_spl
| ~ big_s(X0)
| ~ big_q(X0) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f12,f42,f45]) ).
fof(f49,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f16,f42,f38]) ).
fof(f50,definition,
( sQ8_spl
<=> big_p(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ8_spl
| big_p(sK2_skl) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,definition,
( sQ9_spl
<=> big_q(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ9_spl
| big_q(sK3_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f17,f50,f53]) ).
fof(f57,definition,
( sQ10_spl
<=> big_s(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ10_spl
| ~ big_s(sK3_skl) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( ~ sQ10_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f18,f50,f57]) ).
fof(f61,definition,
( sQ11_spl
<=> big_r(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( sQ11_spl
| ~ big_r(sK2_skl) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ9_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f19,f61,f53]) ).
fof(f65,plain,
( ~ sQ10_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f20,f61,f57]) ).
fof(f66,plain,
( sQ11_spl
| ~ sQ6_spl
| ~ big_p(sK2_skl) ),
inference(resolution,[status(thm)],[f43,f63]) ).
fof(f67,plain,
( sQ11_spl
| ~ sQ6_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f66,f51]) ).
fof(f68,plain,
( sQ11_spl
| ~ sQ6_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f67]) ).
fof(f69,plain,
( sQ10_spl
| ~ sQ5_spl
| ~ big_q(sK3_skl) ),
inference(resolution,[status(thm)],[f39,f59]) ).
fof(f70,plain,
( sQ10_spl
| ~ sQ5_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f54]) ).
fof(f71,plain,
( sQ10_spl
| ~ sQ5_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ5_spl
| ~ big_q(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f46,f39]) ).
fof(f73,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f22]) ).
fof(f74,plain,
( ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f36]) ).
fof(f76,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f75]) ).
fof(f77,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f54,f32]) ).
fof(f79,plain,
( ~ sQ9_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f78]) ).
fof(f80,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f72,f31,f38,f45]) ).
fof(f81,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ7_spl
| ~ big_q(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f46]) ).
fof(f82,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f81]) ).
fof(f83,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f82]) ).
fof(f84,plain,
$false,
inference(sat_refutation,[status(thm)],[f27,f34,f41,f48,f49,f56,f60,f64,f65,f68,f71,f74,f77,f79,f80,f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 10:39:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.054504 seconds
% 0.13/0.42 % CPU time: 0.115391 seconds
% 0.13/0.42 % Total memory used: 16.644 MB
% 0.13/0.42 % Net memory used: 16.131 MB
%------------------------------------------------------------------------------