TSTP Solution File: SET957+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:47 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 5 unt; 0 def)
% Number of atoms : 215 ( 38 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 226 ( 83 ~; 96 |; 31 &)
% ( 12 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 96 ( 72 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C,D] :
~ ( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
~ ( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C,D,E,F] :
( ( subset(A,cartesian_product2(B,C))
& subset(D,cartesian_product2(E,F))
& ! [G,H] :
( in(ordered_pair(G,H),A)
<=> in(ordered_pair(G,H),D) ) )
=> A = D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C,D,E,F] :
( ( subset(A,cartesian_product2(B,C))
& subset(D,cartesian_product2(E,F))
& ! [G,H] :
( in(ordered_pair(G,H),A)
<=> in(ordered_pair(G,H),D) ) )
=> A = D ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [A,B,C,D] :
( ~ subset(A,cartesian_product2(B,C))
| ~ in(D,A)
| ? [E,F] :
( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f24,plain,
! [B,C,D] :
( ! [A] :
( ~ subset(A,cartesian_product2(B,C))
| ~ in(D,A) )
| ? [E,F] :
( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f25,plain,
! [B,C,D] :
( ! [A] :
( ~ subset(A,cartesian_product2(B,C))
| ~ in(D,A) )
| ( in(sk0_2(D,C,B),B)
& in(sk0_3(D,C,B),C)
& D = ordered_pair(sk0_2(D,C,B),sk0_3(D,C,B)) ) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| X3 = ordered_pair(sk0_2(X3,X2,X1),sk0_3(X3,X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f29,plain,
? [A,B,C,D,E,F] :
( subset(A,cartesian_product2(B,C))
& subset(D,cartesian_product2(E,F))
& ! [G,H] :
( in(ordered_pair(G,H),A)
<=> in(ordered_pair(G,H),D) )
& A != D ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f30,plain,
? [A,B,C,D,E,F] :
( subset(A,cartesian_product2(B,C))
& subset(D,cartesian_product2(E,F))
& ! [G,H] :
( ( ~ in(ordered_pair(G,H),A)
| in(ordered_pair(G,H),D) )
& ( in(ordered_pair(G,H),A)
| ~ in(ordered_pair(G,H),D) ) )
& A != D ),
inference(NNF_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
? [A,D] :
( ? [B,C] : subset(A,cartesian_product2(B,C))
& ? [E,F] : subset(D,cartesian_product2(E,F))
& ! [G,H] :
( ~ in(ordered_pair(G,H),A)
| in(ordered_pair(G,H),D) )
& ! [G,H] :
( in(ordered_pair(G,H),A)
| ~ in(ordered_pair(G,H),D) )
& A != D ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
( subset(sk0_4,cartesian_product2(sk0_6,sk0_7))
& subset(sk0_5,cartesian_product2(sk0_8,sk0_9))
& ! [G,H] :
( ~ in(ordered_pair(G,H),sk0_4)
| in(ordered_pair(G,H),sk0_5) )
& ! [G,H] :
( in(ordered_pair(G,H),sk0_4)
| ~ in(ordered_pair(G,H),sk0_5) )
& sk0_4 != sk0_5 ),
inference(skolemization,[status(esa)],[f31]) ).
fof(f33,plain,
subset(sk0_4,cartesian_product2(sk0_6,sk0_7)),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
subset(sk0_5,cartesian_product2(sk0_8,sk0_9)),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sk0_4)
| in(ordered_pair(X0,X1),sk0_5) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f36,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),sk0_4)
| ~ in(ordered_pair(X0,X1),sk0_5) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f37,plain,
sk0_4 != sk0_5,
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f38,plain,
! [A,B] :
( ? [C] :
( in(C,A)
<~> in(C,B) )
| A = B ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f39,plain,
! [A,B] :
( ? [C] :
( ( in(C,A)
| in(C,B) )
& ( ~ in(C,A)
| ~ in(C,B) ) )
| A = B ),
inference(NNF_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [A,B] :
( ( ( in(sk0_10(B,A),A)
| in(sk0_10(B,A),B) )
& ( ~ in(sk0_10(B,A),A)
| ~ in(sk0_10(B,A),B) ) )
| A = B ),
inference(skolemization,[status(esa)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( in(sk0_10(X0,X1),X1)
| in(sk0_10(X0,X1),X0)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ~ in(sk0_10(X0,X1),X1)
| ~ in(sk0_10(X0,X1),X0)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f110,plain,
! [X0] :
( ~ in(X0,sk0_5)
| X0 = ordered_pair(sk0_2(X0,sk0_9,sk0_8),sk0_3(X0,sk0_9,sk0_8)) ),
inference(resolution,[status(thm)],[f28,f34]) ).
fof(f111,plain,
! [X0] :
( ~ in(X0,sk0_4)
| X0 = ordered_pair(sk0_2(X0,sk0_7,sk0_6),sk0_3(X0,sk0_7,sk0_6)) ),
inference(resolution,[status(thm)],[f28,f33]) ).
fof(f114,plain,
! [X0] :
( sk0_10(X0,sk0_5) = ordered_pair(sk0_2(sk0_10(X0,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(X0,sk0_5),sk0_9,sk0_8))
| in(sk0_10(X0,sk0_5),X0)
| sk0_5 = X0 ),
inference(resolution,[status(thm)],[f110,f41]) ).
fof(f115,plain,
! [X0,X1] :
( ordered_pair(X0,X1) = ordered_pair(sk0_2(ordered_pair(X0,X1),sk0_9,sk0_8),sk0_3(ordered_pair(X0,X1),sk0_9,sk0_8))
| ~ in(ordered_pair(X0,X1),sk0_4) ),
inference(resolution,[status(thm)],[f110,f35]) ).
fof(f245,plain,
( spl0_3
<=> sk0_10(sk0_4,sk0_5) = ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f246,plain,
( sk0_10(sk0_4,sk0_5) = ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( spl0_4
<=> sk0_5 = sk0_4 ),
introduced(split_symbol_definition) ).
fof(f249,plain,
( sk0_5 = sk0_4
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,plain,
( spl0_5
<=> sk0_10(sk0_4,sk0_5) = ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6),sk0_3(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6)) ),
introduced(split_symbol_definition) ).
fof(f252,plain,
( sk0_10(sk0_4,sk0_5) = ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6),sk0_3(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( sk0_10(sk0_4,sk0_5) = ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8))
| sk0_5 = sk0_4
| sk0_10(sk0_4,sk0_5) = ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6),sk0_3(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6)) ),
inference(resolution,[status(thm)],[f114,f111]) ).
fof(f255,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f254,f245,f248,f251]) ).
fof(f297,plain,
( spl0_11
<=> in(sk0_10(sk0_4,sk0_5),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f298,plain,
( in(sk0_10(sk0_4,sk0_5),sk0_4)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f299,plain,
( ~ in(sk0_10(sk0_4,sk0_5),sk0_4)
| spl0_11 ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f309,plain,
( spl0_13
<=> in(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6),sk0_3(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6)),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f311,plain,
( ~ in(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6),sk0_3(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6)),sk0_4)
| spl0_13 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f314,plain,
( spl0_14
<=> in(sk0_10(sk0_4,sk0_5),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f315,plain,
( in(sk0_10(sk0_4,sk0_5),sk0_5)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f316,plain,
( ~ in(sk0_10(sk0_4,sk0_5),sk0_5)
| spl0_14 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f319,plain,
( ~ in(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6),sk0_3(sk0_10(sk0_4,sk0_5),sk0_7,sk0_6)),sk0_4)
| in(sk0_10(sk0_4,sk0_5),sk0_5)
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f252,f35]) ).
fof(f320,plain,
( ~ spl0_13
| spl0_14
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f319,f309,f314,f251]) ).
fof(f321,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f37]) ).
fof(f322,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f321]) ).
fof(f335,plain,
( ~ in(sk0_10(sk0_4,sk0_5),sk0_4)
| sk0_5 = sk0_4
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f315,f42]) ).
fof(f336,plain,
( ~ spl0_11
| spl0_4
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f335,f297,f248,f314]) ).
fof(f338,plain,
( sk0_10(sk0_4,sk0_5) = ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8))
| sk0_5 = sk0_4
| spl0_11 ),
inference(resolution,[status(thm)],[f299,f114]) ).
fof(f339,plain,
( spl0_3
| spl0_4
| spl0_11 ),
inference(split_clause,[status(thm)],[f338,f245,f248,f297]) ).
fof(f342,plain,
( ~ in(sk0_10(sk0_4,sk0_5),sk0_4)
| ~ spl0_5
| spl0_13 ),
inference(forward_demodulation,[status(thm)],[f252,f311]) ).
fof(f343,plain,
( in(sk0_10(sk0_4,sk0_5),sk0_4)
| sk0_5 = sk0_4
| spl0_14 ),
inference(resolution,[status(thm)],[f316,f41]) ).
fof(f344,plain,
( spl0_11
| spl0_4
| spl0_14 ),
inference(split_clause,[status(thm)],[f343,f297,f248,f314]) ).
fof(f345,plain,
( $false
| ~ spl0_5
| spl0_13
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f342]) ).
fof(f346,plain,
( ~ spl0_5
| spl0_13
| ~ spl0_11 ),
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f354,plain,
( spl0_15
<=> ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)) = ordered_pair(sk0_2(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_9,sk0_8),sk0_3(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_9,sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f357,plain,
( ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)) = ordered_pair(sk0_2(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_9,sk0_8),sk0_3(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_9,sk0_8))
| ~ in(sk0_10(sk0_4,sk0_5),sk0_4)
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f246,f115]) ).
fof(f358,plain,
( spl0_15
| ~ spl0_11
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f357,f354,f297,f245]) ).
fof(f363,plain,
( spl0_16
<=> in(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f364,plain,
( in(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_4)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f365,plain,
( ~ in(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_4)
| spl0_16 ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f368,plain,
( in(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_4)
| ~ in(sk0_10(sk0_4,sk0_5),sk0_5)
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f246,f36]) ).
fof(f369,plain,
( spl0_16
| ~ spl0_14
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f368,f363,f314,f245]) ).
fof(f370,plain,
( ~ in(ordered_pair(sk0_2(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8),sk0_3(sk0_10(sk0_4,sk0_5),sk0_9,sk0_8)),sk0_4)
| in(sk0_10(sk0_4,sk0_5),sk0_5)
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f246,f35]) ).
fof(f371,plain,
( ~ spl0_16
| spl0_14
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f370,f363,f314,f245]) ).
fof(f375,plain,
( ~ in(sk0_10(sk0_4,sk0_5),sk0_4)
| ~ spl0_3
| spl0_16 ),
inference(forward_demodulation,[status(thm)],[f246,f365]) ).
fof(f376,plain,
( $false
| ~ spl0_3
| spl0_16
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f375]) ).
fof(f377,plain,
( ~ spl0_3
| spl0_16
| ~ spl0_11 ),
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f378,plain,
( in(sk0_10(sk0_4,sk0_5),sk0_4)
| ~ spl0_3
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f246,f364]) ).
fof(f379,plain,
( $false
| spl0_11
| ~ spl0_3
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f299]) ).
fof(f380,plain,
( spl0_11
| ~ spl0_3
| ~ spl0_16 ),
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f381,plain,
$false,
inference(sat_refutation,[status(thm)],[f255,f320,f322,f336,f339,f344,f346,f358,f369,f371,f377,f380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 29 21:55:32 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Drodi V3.6.0
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.053558 seconds
% 0.13/0.40 % CPU time: 0.314420 seconds
% 0.13/0.40 % Total memory used: 64.776 MB
% 0.13/0.40 % Net memory used: 64.638 MB
%------------------------------------------------------------------------------