%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV515+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:32:58 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 31
% Syntax : Number of formulae : 175 ( 4 unt; 26 def)
% Number of atoms : 654 ( 0 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 758 ( 279 ~; 349 |; 100 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 32 ( 31 usr; 24 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 181 ( 162 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ~ ? [A] :
! [B] :
( ( g_true_only(B,B)
& g_false_only(B,A) )
| ( g_false_only(B,B)
& g_true_only(B,A) ) )
& ? [A] :
( ~ ? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) )
& ? [B] :
( g_both(B,B)
& g_both(B,A) ) ) )
| ! [A] :
? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [A] :
! [B] :
( ( g_true_only(B,B)
& g_false_only(B,A) )
| ( g_false_only(B,B)
& g_true_only(B,A) ) )
& ? [A] :
( ~ ? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) )
& ? [B] :
( g_both(B,B)
& g_both(B,A) ) ) )
| ! [A] :
? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X_2,X_1] :
( g_true_only(X_2,X_1)
<=> ( ~ g_false(X_2,X_1)
& g_true(X_2,X_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X_2,X_1] :
( g_both(X_2,X_1)
<=> ( g_false(X_2,X_1)
& g_true(X_2,X_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X_2,X_1] :
( g_false_only(X_2,X_1)
<=> ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X_2,X_1] :
( g_false_only(X_2,X_1)
| g_both(X_2,X_1)
| g_true_only(X_2,X_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
( ( ? [A] :
! [B] :
( ( g_true_only(B,B)
& g_false_only(B,A) )
| ( g_false_only(B,B)
& g_true_only(B,A) ) )
| ! [A] :
( ? [B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) )
| ! [B] :
( ~ g_both(B,B)
| ~ g_both(B,A) ) ) )
& ? [A] :
! [B] :
( ( ( ~ g_both(B,B)
& ~ g_false_only(B,B) )
| ~ g_false_only(B,A) )
& ( ( ~ g_true_only(B,B)
& ~ g_false_only(B,B) )
| ~ g_both(B,A) )
& ( ( ~ g_true_only(B,B)
& ~ g_both(B,B) )
| ~ g_true_only(B,A) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f8,definition,
! [A,B] :
( sP0_prd(B,A)
<=> ( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f9,definition,
! [A,B] :
( sP1_prd(B,A)
<=> ( g_false_only(B,B)
& g_true_only(B,A) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f10,plain,
( ( ? [A] :
! [B] :
( ( g_true_only(B,B)
& g_false_only(B,A) )
| sP1_prd(B,A) )
| ! [A] :
( ? [B] : sP0_prd(B,A)
| ! [B] :
( ~ g_both(B,B)
| ~ g_both(B,A) ) ) )
& ? [A] :
! [B] :
( ( ( ~ g_both(B,B)
& ~ g_false_only(B,B) )
| ~ g_false_only(B,A) )
& ( ( ~ g_true_only(B,B)
& ~ g_false_only(B,B) )
| ~ g_both(B,A) )
& ( ( ~ g_true_only(B,B)
& ~ g_both(B,B) )
| ~ g_true_only(B,A) ) ) ),
inference(formula_renaming,[status(thm)],[f7,f9,f8]) ).
fof(f11,plain,
( ( ? [A] :
! [B] :
( ( g_true_only(B,B)
& g_false_only(B,A) )
| sP1_prd(B,A) )
| ! [A] :
( ? [B] : sP0_prd(B,A)
| ! [B] :
( ~ g_both(B,B)
| ~ g_both(B,A) ) ) )
& ? [A] :
( ! [B] :
( ( ~ g_both(B,B)
& ~ g_false_only(B,B) )
| ~ g_false_only(B,A) )
& ! [B] :
( ( ~ g_true_only(B,B)
& ~ g_false_only(B,B) )
| ~ g_both(B,A) )
& ! [B] :
( ( ~ g_true_only(B,B)
& ~ g_both(B,B) )
| ~ g_true_only(B,A) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f12,plain,
( ( ! [B] :
( ( g_true_only(B,B)
& g_false_only(B,sK2_skl) )
| sP1_prd(B,sK2_skl) )
| ! [A] :
( sP0_prd(sK1_skl(A),A)
| ! [B] :
( ~ g_both(B,B)
| ~ g_both(B,A) ) ) )
& ! [B] :
( ( ~ g_both(B,B)
& ~ g_false_only(B,B) )
| ~ g_false_only(B,sK0_skl) )
& ! [B] :
( ( ~ g_true_only(B,B)
& ~ g_false_only(B,B) )
| ~ g_both(B,sK0_skl) )
& ! [B] :
( ( ~ g_true_only(B,B)
& ~ g_both(B,B) )
| ~ g_true_only(B,sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl(A)),skolemize(A,sK2_skl)],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ g_both(X0,X0)
| ~ g_true_only(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ g_true_only(X0,X0)
| ~ g_true_only(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0] :
( ~ g_false_only(X0,X0)
| ~ g_both(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [X0] :
( ~ g_true_only(X0,X0)
| ~ g_both(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f17,plain,
! [X0] :
( ~ g_false_only(X0,X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f18,plain,
! [X0] :
( ~ g_both(X0,X0)
| ~ g_false_only(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f20,plain,
! [X0,X1,X2] :
( g_true_only(X2,X2)
| sP1_prd(X2,sK2_skl)
| sP0_prd(sK1_skl(X1),X1)
| ~ g_both(X0,X0)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f21,plain,
! [X_2,X_1] :
( ( g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_true_only(X_2,X_1) )
& ( ( ~ g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_true_only(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
( ! [X_2,X_1] :
( g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_true_only(X_2,X_1) )
& ! [X_2,X_1] :
( ( ~ g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_true_only(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [X_2,X_1] :
( ( ~ g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_both(X_2,X_1) )
& ( ( g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_both(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
( ! [X_2,X_1] :
( ~ g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_both(X_2,X_1) )
& ! [X_2,X_1] :
( ( g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_both(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X_2,X_1] :
( ( g_true(X_2,X_1)
| ~ g_false(X_2,X_1)
| g_false_only(X_2,X_1) )
& ( ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) )
| ~ g_false_only(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
( ! [X_2,X_1] :
( g_true(X_2,X_1)
| ~ g_false(X_2,X_1)
| g_false_only(X_2,X_1) )
& ! [X_2,X_1] :
( ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) )
| ~ g_false_only(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f37,definition,
! [A,B] :
( sP2_prd(B,A)
<=> ( ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f38,plain,
! [A,B] :
( sP0_prd(B,A)
<=> ( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| sP2_prd(B,A) ) ),
inference(formula_renaming,[status(thm)],[f8,f37]) ).
fof(f39,plain,
! [A,B] :
( ( ( ( ( ~ g_both(B,B)
& ~ g_false_only(B,B) )
| ~ g_false_only(B,A) )
& ~ sP2_prd(B,A) )
| sP0_prd(B,A) )
& ( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| sP2_prd(B,A)
| ~ sP0_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( ( ( ( ~ g_both(B,B)
& ~ g_false_only(B,B) )
| ~ g_false_only(B,A) )
& ~ sP2_prd(B,A) )
| sP0_prd(B,A) )
& ! [A,B] :
( ( ( g_both(B,B)
| g_false_only(B,B) )
& g_false_only(B,A) )
| sP2_prd(B,A)
| ~ sP0_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| sP2_prd(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( g_both(X0,X0)
| g_false_only(X0,X0)
| sP2_prd(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( ~ g_false_only(X0,X0)
| ~ g_false_only(X0,X1)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ~ g_both(X0,X0)
| ~ g_false_only(X0,X1)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f46,plain,
! [A,B] :
( ( ~ g_false_only(B,B)
| ~ g_true_only(B,A)
| sP1_prd(B,A) )
& ( ( g_false_only(B,B)
& g_true_only(B,A) )
| ~ sP1_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f47,plain,
( ! [A,B] :
( ~ g_false_only(B,B)
| ~ g_true_only(B,A)
| sP1_prd(B,A) )
& ! [A,B] :
( ( g_false_only(B,B)
& g_true_only(B,A) )
| ~ sP1_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( g_true_only(X0,X1)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( g_false_only(X0,X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
! [A,B] :
( ( ( ( ( ~ g_true_only(B,B)
& ~ g_false_only(B,B) )
| ~ g_both(B,A) )
& ( ( ~ g_true_only(B,B)
& ~ g_both(B,B) )
| ~ g_true_only(B,A) ) )
| sP2_prd(B,A) )
& ( ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) )
| ~ sP2_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f52,plain,
( ! [A,B] :
( ( ( ( ~ g_true_only(B,B)
& ~ g_false_only(B,B) )
| ~ g_both(B,A) )
& ( ( ~ g_true_only(B,B)
& ~ g_both(B,B) )
| ~ g_true_only(B,A) ) )
| sP2_prd(B,A) )
& ! [A,B] :
( ( ( g_true_only(B,B)
| g_false_only(B,B) )
& g_both(B,A) )
| ( ( g_true_only(B,B)
| g_both(B,B) )
& g_true_only(B,A) )
| ~ sP2_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( g_both(X0,X1)
| g_true_only(X0,X1)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( g_true_only(X0,X0)
| g_false_only(X0,X0)
| g_true_only(X0,X1)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( g_both(X0,X1)
| g_true_only(X0,X0)
| g_both(X0,X0)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [X0,X1] :
( ~ g_both(X0,X0)
| ~ g_true_only(X0,X1)
| sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f61,definition,
! [X0,X1] :
( sQ0_spl
<=> ( sP0_prd(sK1_skl(X1),X1)
| ~ g_both(X0,X0)
| ~ g_both(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f62,plain,
! [X0,X1] :
( ~ sQ0_spl
| sP0_prd(sK1_skl(X1),X1)
| ~ g_both(X0,X0)
| ~ g_both(X0,X1) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f68,definition,
! [X2] :
( sQ2_spl
<=> ( g_true_only(X2,X2)
| sP1_prd(X2,sK2_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f69,plain,
! [X0] :
( ~ sQ2_spl
| g_true_only(X0,X0)
| sP1_prd(X0,sK2_skl) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f61,f68]) ).
fof(f75,definition,
( sQ3_spl
<=> g_false_only(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ3_spl
| g_false_only(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f77,plain,
( sQ3_spl
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
! [X0] :
( sQ4_spl
<=> ~ sP1_prd(sK0_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f79,plain,
! [X0] :
( ~ sQ4_spl
| ~ sP1_prd(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f83,plain,
( sQ3_spl
| g_both(sK0_skl,sK0_skl)
| g_true_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f36,f77]) ).
fof(f84,plain,
! [X0] :
( ~ g_false_only(X0,X0)
| g_both(X0,sK0_skl)
| g_true_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f36,f17]) ).
fof(f85,definition,
( sQ5_spl
<=> g_true_only(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ5_spl
| g_true_only(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ5_spl
| ~ g_true_only(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ6_spl
<=> g_both(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ6_spl
| g_both(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( sQ3_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f83,f85,f88,f75]) ).
fof(f92,plain,
! [X0] :
( ~ g_false_only(X0,X0)
| g_true_only(X0,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f15]) ).
fof(f102,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[f29,f24]) ).
fof(f106,plain,
! [X0] :
( g_both(X0,X0)
| g_true_only(X0,X0)
| g_true_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f92,f36]) ).
fof(f108,plain,
! [X0,X1] :
( g_both(X0,X0)
| g_true_only(X0,X0)
| ~ g_false_only(X0,X1)
| sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f44,f36]) ).
fof(f110,plain,
! [X0] :
( ~ sQ6_spl
| ~ g_false_only(sK0_skl,X0)
| sP0_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f45,f89]) ).
fof(f112,plain,
! [X0] :
( ~ sQ6_spl
| ~ sP1_prd(sK0_skl,X0)
| sP0_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f110,f49]) ).
fof(f113,definition,
( sQ7_spl
<=> sP0_prd(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ7_spl
| sP0_prd(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( ~ sQ6_spl
| sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f112,f113,f78,f88]) ).
fof(f117,plain,
( ~ sQ7_spl
| g_false_only(sK0_skl,sK0_skl)
| sP2_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f114,f41]) ).
fof(f118,definition,
( sQ8_spl
<=> sP2_prd(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ8_spl
| sP2_prd(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( ~ sQ7_spl
| sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f117,f118,f75,f113]) ).
fof(f122,plain,
( ~ sQ5_spl
| ~ g_true_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f86,f14]) ).
fof(f123,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f86]) ).
fof(f124,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f123]) ).
fof(f125,plain,
( ~ sQ3_spl
| ~ g_false_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f76,f17]) ).
fof(f128,plain,
~ sQ3_spl,
inference(split_clause,[status(thm)],[f125,f75]) ).
fof(f146,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(resolution,[status(thm)],[f33,f24]) ).
fof(f147,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(resolution,[status(thm)],[f34,f28]) ).
fof(f154,plain,
( ~ sQ8_spl
| g_true_only(sK0_skl,sK0_skl)
| g_false_only(sK0_skl,sK0_skl)
| g_true_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f54,f119]) ).
fof(f155,plain,
( ~ sQ8_spl
| sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f154,f85,f75,f118]) ).
fof(f165,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| sP0_prd(sK1_skl(X0),X0)
| ~ g_both(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f62,f89]) ).
fof(f167,plain,
! [X0,X1] :
( ~ sP1_prd(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(resolution,[status(thm)],[f146,f48]) ).
fof(f169,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sP0_prd(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f165,f89]) ).
fof(f170,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| g_both(sK1_skl(sK0_skl),sK1_skl(sK0_skl))
| g_false_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl))
| sP2_prd(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f169,f42]) ).
fof(f171,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| g_false_only(sK1_skl(sK0_skl),sK0_skl)
| sP2_prd(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f169,f41]) ).
fof(f172,definition,
( sQ9_spl
<=> sP2_prd(sK1_skl(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ9_spl
| sP2_prd(sK1_skl(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
( sQ10_spl
<=> g_false_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f178,definition,
( sQ11_spl
<=> g_both(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( ~ sQ11_spl
| g_both(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f170,f172,f175,f178,f61,f88]) ).
fof(f182,definition,
( sQ12_spl
<=> g_false_only(sK1_skl(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ12_spl
| g_false_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sQ12_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f171,f172,f182,f61,f88]) ).
fof(f186,plain,
( ~ sQ9_spl
| g_both(sK1_skl(sK0_skl),sK0_skl)
| g_true_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl))
| g_both(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f173,f55]) ).
fof(f187,plain,
( ~ sQ9_spl
| g_true_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl))
| g_false_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl))
| g_true_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f173,f54]) ).
fof(f188,plain,
( ~ sQ9_spl
| g_both(sK1_skl(sK0_skl),sK0_skl)
| g_true_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f173,f53]) ).
fof(f190,definition,
( sQ13_spl
<=> g_true_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( ~ sQ13_spl
| g_true_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ14_spl
<=> g_both(sK1_skl(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ14_spl
| g_both(sK1_skl(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( ~ sQ9_spl
| sQ14_spl
| sQ13_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f186,f178,f190,f193,f172]) ).
fof(f197,definition,
( sQ15_spl
<=> g_true_only(sK1_skl(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ15_spl
| g_true_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( ~ sQ9_spl
| sQ13_spl
| sQ10_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f187,f197,f175,f190,f172]) ).
fof(f201,plain,
( ~ sQ9_spl
| sQ14_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f188,f197,f193,f172]) ).
fof(f203,plain,
( ~ sQ14_spl
| ~ g_false_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f194,f15]) ).
fof(f204,plain,
( ~ sQ14_spl
| ~ g_false_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f194,f147]) ).
fof(f205,plain,
( ~ sQ14_spl
| ~ g_true_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f194,f102]) ).
fof(f211,definition,
( sQ16_spl
<=> sP1_prd(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ16_spl
| sP1_prd(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f218,definition,
( sQ18_spl
<=> sP1_prd(sK2_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ18_spl
| sP1_prd(sK2_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f229,plain,
( ~ sQ16_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f79]) ).
fof(f230,plain,
( ~ sQ16_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f231,plain,
( sQ5_spl
| ~ sQ2_spl
| sP1_prd(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f69,f87]) ).
fof(f238,plain,
( sQ5_spl
| ~ sQ2_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f231,f211,f68,f85]) ).
fof(f243,plain,
( ~ sQ18_spl
| ~ g_false_only(sK2_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f219,f167]) ).
fof(f265,plain,
! [X0,X1] :
( g_true_only(X0,X0)
| ~ g_false_only(X0,X1)
| sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f45]) ).
fof(f266,plain,
! [X0,X1] :
( g_both(X0,X1)
| g_true_only(X0,X1)
| g_true_only(X0,X0)
| sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f265,f36]) ).
fof(f269,plain,
! [X0] :
( ~ sQ18_spl
| ~ sP1_prd(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f243,f49]) ).
fof(f277,plain,
( ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f219,f269]) ).
fof(f278,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f277]) ).
fof(f377,plain,
! [X0,X1] :
( ~ sQ0_spl
| sP0_prd(sK1_skl(X1),X1)
| ~ g_both(X0,X1)
| g_true_only(X0,X0)
| g_true_only(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f106,f62]) ).
fof(f389,plain,
! [X0] :
( sQ5_spl
| g_both(sK0_skl,X0)
| g_true_only(sK0_skl,X0)
| sP0_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f266,f87]) ).
fof(f406,plain,
! [X0] :
( ~ g_true_only(X0,sK0_skl)
| g_true_only(X0,X0)
| g_true_only(X0,X0)
| sP0_prd(X0,X0) ),
inference(resolution,[status(thm)],[f266,f13]) ).
fof(f407,definition,
! [X0] :
( sQ34_spl
<=> ( g_both(sK0_skl,X0)
| g_true_only(sK0_skl,X0)
| sP0_prd(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f420,plain,
! [X0] :
( ~ g_true_only(X0,sK0_skl)
| g_true_only(X0,X0)
| sP0_prd(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f406]) ).
fof(f421,plain,
! [X0] :
( ~ g_true_only(X0,sK0_skl)
| sP0_prd(X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f420,f14]) ).
fof(f506,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sP0_prd(sK1_skl(sK0_skl),sK0_skl)
| g_true_only(sK0_skl,sK0_skl)
| g_true_only(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f377,f89]) ).
fof(f509,definition,
( sQ37_spl
<=> sP0_prd(sK1_skl(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sQ37_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f506,f85,f509,f61,f88]) ).
fof(f558,plain,
! [X0] :
( ~ sQ0_spl
| sQ5_spl
| sP0_prd(sK1_skl(X0),X0)
| g_true_only(sK0_skl,sK0_skl)
| g_true_only(sK0_skl,sK0_skl)
| g_true_only(sK0_skl,X0)
| sP0_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f389,f377]) ).
fof(f559,plain,
! [X0] :
( ~ sQ0_spl
| sQ5_spl
| sP0_prd(sK1_skl(X0),X0)
| ~ g_both(sK0_skl,X0)
| g_true_only(sK0_skl,sK0_skl)
| sP0_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f389,f62]) ).
fof(f563,plain,
! [X0] :
( sQ5_spl
| ~ g_true_only(sK0_skl,X0)
| sP2_prd(sK0_skl,X0)
| g_true_only(sK0_skl,sK0_skl)
| sP0_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f389,f57]) ).
fof(f564,plain,
! [X0] :
( sQ5_spl
| ~ g_false_only(sK0_skl,X0)
| sP0_prd(sK0_skl,X0)
| g_true_only(sK0_skl,sK0_skl)
| sP0_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f389,f45]) ).
fof(f570,definition,
! [X0] :
( sQ38_spl
<=> ( sP0_prd(sK1_skl(X0),X0)
| g_true_only(sK0_skl,X0)
| sP0_prd(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( ~ sQ0_spl
| sQ5_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f558,f570,f85,f61]) ).
fof(f574,definition,
! [X0] :
( sQ39_spl
<=> ( sP0_prd(sK1_skl(X0),X0)
| ~ g_both(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( ~ sQ0_spl
| sQ39_spl
| sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f559,f113,f85,f574,f61]) ).
fof(f582,definition,
! [X0] :
( sQ41_spl
<=> ( ~ g_true_only(sK0_skl,X0)
| sP2_prd(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ41_spl
| sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f563,f113,f85,f582]) ).
fof(f586,definition,
! [X0] :
( sQ42_spl
<=> ( ~ g_false_only(sK0_skl,X0)
| sP0_prd(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ42_spl
| sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f564,f113,f85,f586]) ).
fof(f593,plain,
( ~ sQ15_spl
| ~ g_true_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f198,f14]) ).
fof(f595,plain,
( ~ sQ15_spl
| ~ g_false_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f198,f146]) ).
fof(f606,plain,
( ~ sQ12_spl
| ~ g_false_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f183,f17]) ).
fof(f608,plain,
( ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f606,f175,f182]) ).
fof(f614,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f183]) ).
fof(f615,plain,
( ~ sQ15_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f614]) ).
fof(f616,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f183]) ).
fof(f617,plain,
( ~ sQ14_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f637,plain,
! [X0] :
( g_both(sK0_skl,X0)
| g_true_only(sK0_skl,X0)
| sP0_prd(sK0_skl,X0)
| sP0_prd(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f421,f266]) ).
fof(f639,plain,
( sQ34_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f637,f113,f407]) ).
fof(f649,plain,
( ~ sQ11_spl
| ~ g_false_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f179,f18]) ).
fof(f650,plain,
( ~ sQ11_spl
| ~ g_true_only(sK1_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f179,f13]) ).
fof(f663,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f649,f183]) ).
fof(f664,plain,
( ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f663]) ).
fof(f729,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f593,f191]) ).
fof(f730,plain,
( ~ sQ15_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f731,plain,
( ~ sQ11_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f650,f197,f178]) ).
fof(f732,plain,
( ~ sQ14_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f205,f197,f193]) ).
fof(f733,plain,
( ~ sQ14_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f203,f175,f193]) ).
fof(f734,plain,
( ~ sQ14_spl
| ~ g_true_only(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f194,f16]) ).
fof(f742,plain,
( ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f734,f190,f193]) ).
fof(f747,plain,
$false,
inference(sat_refutation,[status(thm)],[f71,f91,f116,f121,f124,f128,f155,f181,f185,f196,f200,f201,f230,f238,f278,f513,f573,f577,f585,f589,f608,f615,f617,f639,f664,f730,f731,f732,f733,f742]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV515+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:24:27 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.047031 seconds
% 0.12/0.42 % CPU time: 0.181852 seconds
% 0.12/0.42 % Total memory used: 18.728 MB
% 0.12/0.42 % Net memory used: 18.516 MB
%------------------------------------------------------------------------------