%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO607+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 : n014.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 03:42:49 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 84 ( 8 unt; 15 def)
% Number of atoms : 280 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 323 ( 127 ~; 137 |; 44 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-1 aty)
% Number of variables : 132 ( 90 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ~ ? [A] :
! [B] : g_true_only(A,B)
& ? [A] :
( ~ ? [B] : g_false_only(A,B)
& ? [B] : g_both(A,B) )
& ~ ? [A] :
( ? [B] : g_false_only(A,B)
& g_false_only(a,A) )
& ? [A] :
( ~ ! [B] : g_true_only(A,B)
& ~ g_true_only(a,A)
& ( ( ~ ? [B] : g_false_only(A,B)
& ? [B] : g_both(A,B) )
| g_both(a,A) ) ) )
| ? [A] :
! [B] : g_true_only(A,B)
| ? [A] :
( ? [B] : g_false_only(A,B)
& g_false_only(a,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [A] :
! [B] : g_true_only(A,B)
& ? [A] :
( ~ ? [B] : g_false_only(A,B)
& ? [B] : g_both(A,B) )
& ~ ? [A] :
( ? [B] : g_false_only(A,B)
& g_false_only(a,A) )
& ? [A] :
( ~ ! [B] : g_true_only(A,B)
& ~ g_true_only(a,A)
& ( ( ~ ? [B] : g_false_only(A,B)
& ? [B] : g_both(A,B) )
| g_both(a,A) ) ) )
| ? [A] :
! [B] : g_true_only(A,B)
| ? [A] :
( ? [B] : g_false_only(A,B)
& g_false_only(a,A) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
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(A,B)
| ! [A] :
( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) )
| ? [A] :
( ? [B] : g_false_only(A,B)
& g_false_only(a,A) )
| ! [A] :
( ! [B] : g_true_only(A,B)
| g_true_only(a,A)
| ( ( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ~ g_both(a,A) ) ) )
& ! [A] :
? [B] : ~ g_true_only(A,B)
& ! [A] :
( ! [B] : ~ g_false_only(A,B)
| ~ g_false_only(a,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f8,definition,
! [A] :
( sP0_prd(A)
<=> ( ! [B] : g_true_only(A,B)
| g_true_only(a,A)
| ( ( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ~ g_both(a,A) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f9,plain,
( ( ? [A] :
! [B] : g_true_only(A,B)
| ! [A] :
( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) )
| ? [A] :
( ? [B] : g_false_only(A,B)
& g_false_only(a,A) )
| ! [A] : sP0_prd(A) )
& ! [A] :
? [B] : ~ g_true_only(A,B)
& ! [A] :
( ! [B] : ~ g_false_only(A,B)
| ~ g_false_only(a,A) ) ),
inference(formula_renaming,[status(thm)],[f7,f8]) ).
fof(f10,plain,
( ( ! [B] : g_true_only(sK4_skl,B)
| ! [A] :
( g_false_only(A,sK3_skl(A))
| ! [B] : ~ g_both(A,B) )
| ( g_false_only(sK1_skl,sK2_skl)
& g_false_only(a,sK1_skl) )
| ! [A] : sP0_prd(A) )
& ! [A] : ~ g_true_only(A,sK0_skl(A))
& ! [A] :
( ! [B] : ~ g_false_only(A,B)
| ~ g_false_only(a,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK0_skl(A)),skolemize(A,sK1_skl),skolemize(B,sK2_skl),skolemize(B,sK3_skl(A)),skolemize(A,sK4_skl)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_false_only(a,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] : ~ g_true_only(X0,sK0_skl(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( g_true_only(sK4_skl,X3)
| g_false_only(X1,sK3_skl(X1))
| ~ g_both(X1,X2)
| g_false_only(a,sK1_skl)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( g_true_only(sK4_skl,X3)
| g_false_only(X1,sK3_skl(X1))
| ~ g_both(X1,X2)
| g_false_only(sK1_skl,sK2_skl)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
! [A] :
( ( ( ? [B] : ~ g_true_only(A,B)
& ~ g_true_only(a,A)
& ( ( ! [B] : ~ g_false_only(A,B)
& ? [B] : g_both(A,B) )
| g_both(a,A) ) )
| sP0_prd(A) )
& ( ! [B] : g_true_only(A,B)
| g_true_only(a,A)
| ( ( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ~ g_both(a,A) )
| ~ sP0_prd(A) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
( ! [A] :
( ( ? [B] : ~ g_true_only(A,B)
& ~ g_true_only(a,A)
& ( ( ! [B] : ~ g_false_only(A,B)
& ? [B] : g_both(A,B) )
| g_both(a,A) ) )
| sP0_prd(A) )
& ! [A] :
( ! [B] : g_true_only(A,B)
| g_true_only(a,A)
| ( ( ? [B] : g_false_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ~ g_both(a,A) )
| ~ sP0_prd(A) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [A] :
( ( ~ g_true_only(A,sK7_skl(A))
& ~ g_true_only(a,A)
& ( ( ! [B] : ~ g_false_only(A,B)
& g_both(A,sK6_skl(A)) )
| g_both(a,A) ) )
| sP0_prd(A) )
& ! [A] :
( ! [B] : g_true_only(A,B)
| g_true_only(a,A)
| ( ( g_false_only(A,sK5_skl(A))
| ! [B] : ~ g_both(A,B) )
& ~ g_both(a,A) )
| ~ sP0_prd(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(B,sK5_skl(A)),skolemize(B,sK6_skl(A)),skolemize(B,sK7_skl(A))],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( g_true_only(X0,X1)
| g_true_only(a,X0)
| ~ g_both(a,X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( g_true_only(X0,X2)
| g_true_only(a,X0)
| g_false_only(X0,sK5_skl(X0))
| ~ g_both(X0,X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f40,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f41,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f40]) ).
fof(f43,definition,
( sQ1_spl
<=> g_false_only(a,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ1_spl
| g_false_only(a,sK1_skl) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,definition,
! [X1,X2] :
( sQ2_spl
<=> ( g_false_only(X1,sK3_skl(X1))
| ~ g_both(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f47,plain,
! [X0,X1] :
( ~ sQ2_spl
| g_false_only(X0,sK3_skl(X0))
| ~ g_both(X0,X1) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
! [X3] :
( sQ3_spl
<=> g_true_only(sK4_skl,X3) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f50,plain,
! [X0] :
( ~ sQ3_spl
| g_true_only(sK4_skl,X0) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f13,f40,f43,f46,f49]) ).
fof(f53,definition,
( sQ4_spl
<=> g_false_only(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ4_spl
| g_false_only(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ3_spl
| sQ2_spl
| sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f40,f53,f46,f49]) ).
fof(f57,plain,
( ~ sQ3_spl
| $false ),
inference(resolution,[status(thm)],[f12,f50]) ).
fof(f58,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0] :
( g_false_only(X0,sK0_skl(X0))
| g_both(X0,sK0_skl(X0)) ),
inference(resolution,[status(thm)],[f30,f12]) ).
fof(f60,plain,
! [X0] :
( ~ g_false_only(sK0_skl(a),X0)
| g_both(a,sK0_skl(a)) ),
inference(resolution,[status(thm)],[f59,f11]) ).
fof(f63,definition,
( sQ5_spl
<=> g_both(a,sK0_skl(a)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ5_spl
| g_both(a,sK0_skl(a)) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
! [X0] :
( sQ6_spl
<=> ~ g_false_only(sK0_skl(a),X0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f67,plain,
! [X0] :
( ~ sQ6_spl
| ~ g_false_only(sK0_skl(a),X0) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f60,f63,f66]) ).
fof(f75,plain,
! [X0] :
( ~ sQ5_spl
| g_true_only(sK0_skl(a),X0)
| g_true_only(a,sK0_skl(a))
| ~ sP0_prd(sK0_skl(a)) ),
inference(resolution,[status(thm)],[f64,f34]) ).
fof(f78,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| g_false_only(a,sK3_skl(a)) ),
inference(resolution,[status(thm)],[f64,f47]) ).
fof(f79,definition,
( sQ7_spl
<=> sP0_prd(sK0_skl(a)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( sQ7_spl
| ~ sP0_prd(sK0_skl(a)) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,definition,
( sQ8_spl
<=> g_true_only(a,sK0_skl(a)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ8_spl
| g_true_only(a,sK0_skl(a)) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
! [X0] :
( sQ9_spl
<=> g_true_only(sK0_skl(a),X0) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f86,plain,
! [X0] :
( ~ sQ9_spl
| g_true_only(sK0_skl(a),X0) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( ~ sQ5_spl
| sQ9_spl
| sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f75,f79,f82,f85,f63]) ).
fof(f98,definition,
! [X0] :
( sQ13_spl
<=> g_true_only(a,X0) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f99,plain,
! [X0] :
( ~ sQ13_spl
| g_true_only(a,X0) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f106,plain,
( ~ sQ13_spl
| $false ),
inference(resolution,[status(thm)],[f99,f12]) ).
fof(f107,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f108,plain,
( ~ sQ9_spl
| $false ),
inference(resolution,[status(thm)],[f86,f12]) ).
fof(f109,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ g_false_only(sK3_skl(a),X0) ),
inference(resolution,[status(thm)],[f78,f11]) ).
fof(f113,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| g_both(sK3_skl(a),sK0_skl(sK3_skl(a))) ),
inference(resolution,[status(thm)],[f110,f59]) ).
fof(f126,plain,
! [X0] :
( ~ sQ1_spl
| ~ g_false_only(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f44,f11]) ).
fof(f130,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f126]) ).
fof(f131,plain,
( ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f132,plain,
( sQ7_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f81,f41]) ).
fof(f133,plain,
( sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f134,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f12]) ).
fof(f135,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f136,plain,
( ~ sQ6_spl
| g_both(sK0_skl(a),sK0_skl(sK0_skl(a))) ),
inference(resolution,[status(thm)],[f67,f59]) ).
fof(f140,plain,
! [X0] :
( ~ sQ6_spl
| g_true_only(sK0_skl(a),X0)
| g_true_only(a,sK0_skl(a))
| g_false_only(sK0_skl(a),sK5_skl(sK0_skl(a)))
| ~ sP0_prd(sK0_skl(a)) ),
inference(resolution,[status(thm)],[f136,f35]) ).
fof(f141,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| g_false_only(sK0_skl(a),sK3_skl(sK0_skl(a))) ),
inference(resolution,[status(thm)],[f136,f47]) ).
fof(f143,definition,
( sQ16_spl
<=> g_false_only(sK0_skl(a),sK5_skl(sK0_skl(a))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ16_spl
| g_false_only(sK0_skl(a),sK5_skl(sK0_skl(a))) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( ~ sQ6_spl
| sQ9_spl
| sQ8_spl
| sQ16_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f140,f79,f143,f82,f85,f66]) ).
fof(f147,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f67]) ).
fof(f148,plain,
( ~ sQ2_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,plain,
( ~ sQ16_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f67]) ).
fof(f150,plain,
( ~ sQ16_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f196,definition,
! [X0] :
( sQ23_spl
<=> g_true_only(sK3_skl(a),X0) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f197,plain,
! [X0] :
( ~ sQ23_spl
| g_true_only(sK3_skl(a),X0) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f229,definition,
! [X0] :
( sQ26_spl
<=> g_true_only(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f230,plain,
! [X0] :
( ~ sQ26_spl
| g_true_only(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f246,plain,
( ~ sQ26_spl
| $false ),
inference(resolution,[status(thm)],[f230,f12]) ).
fof(f247,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f276,plain,
( ~ sQ23_spl
| $false ),
inference(resolution,[status(thm)],[f197,f12]) ).
fof(f277,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f312,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| g_false_only(sK3_skl(a),sK3_skl(sK3_skl(a))) ),
inference(resolution,[status(thm)],[f113,f47]) ).
fof(f315,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f110]) ).
fof(f316,plain,
( ~ sQ2_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f317,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f56,f58,f69,f88,f107,f109,f131,f133,f135,f146,f148,f150,f247,f277,f316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 12:03:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.040312 seconds
% 0.13/0.41 % CPU time: 0.120741 seconds
% 0.13/0.41 % Total memory used: 17.284 MB
% 0.13/0.41 % Net memory used: 16.926 MB
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