%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 08:57:27 AM UTC 2026
% Result : Theorem 0.14s 10.88s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 60 ( 26 unt; 0 def)
% Number of atoms : 395 ( 32 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 508 ( 173 ~; 163 |; 160 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 189 ( 1 sgn 128 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(order,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,X)
& apply(R,X,Y) )
=> X = Y ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('SET006+3.ax',order) ).
fof(least,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,M,X) )
& member(M,E) ) ),
file('SET006+3.ax',least) ).
fof(thIV2,conjecture,
! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
file('theBenchmark.p',thIV2) ).
fof(f_1_1,plain,
! [R,E] :
( ( order(R,E)
| ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ? [X,Y] :
( X != Y
& apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ? [X] :
( ~ apply(R,X,X)
& member(X,E) ) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) )
| ~ order(R,E) ) ),
inference(fof_nnf,[status(thm)],[order]) ).
fof(f_1_2,plain,
! [U_13,U_12] :
( ( order(U_13,U_12)
| ? [U_11,U_10,U_9] :
( ~ apply(U_13,U_11,U_9)
& apply(U_13,U_10,U_9)
& apply(U_13,U_11,U_10)
& member(U_9,U_12)
& member(U_10,U_12)
& member(U_11,U_12) )
| ? [U_8,U_7] :
( U_8 != U_7
& apply(U_13,U_7,U_8)
& apply(U_13,U_8,U_7)
& member(U_7,U_12)
& member(U_8,U_12) )
| ? [U_6] :
( ~ apply(U_13,U_6,U_6)
& member(U_6,U_12) ) )
& ( ( ! [U_5,U_4,U_3] :
( apply(U_13,U_5,U_3)
| ~ apply(U_13,U_4,U_3)
| ~ apply(U_13,U_5,U_4)
| ~ member(U_3,U_12)
| ~ member(U_4,U_12)
| ~ member(U_5,U_12) )
& ! [U_2,U_1] :
( U_2 = U_1
| ~ apply(U_13,U_1,U_2)
| ~ apply(U_13,U_2,U_1)
| ~ member(U_1,U_12)
| ~ member(U_2,U_12) )
& ! [U_0] :
( apply(U_13,U_0,U_0)
| ~ member(U_0,U_12) ) )
| ~ order(U_13,U_12) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_17,U_15] :
( order(U_17,U_15)
| ? [U_11,U_10,U_9] :
( ~ apply(U_17,U_11,U_9)
& apply(U_17,U_10,U_9)
& apply(U_17,U_11,U_10)
& member(U_9,U_15)
& member(U_10,U_15)
& member(U_11,U_15) )
| ? [U_8,U_7] :
( U_8 != U_7
& apply(U_17,U_7,U_8)
& apply(U_17,U_8,U_7)
& member(U_7,U_15)
& member(U_8,U_15) )
| ? [U_6] :
( ~ apply(U_17,U_6,U_6)
& member(U_6,U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_5,U_4,U_3] :
( apply(U_16,U_5,U_3)
| ~ apply(U_16,U_4,U_3)
| ~ apply(U_16,U_5,U_4)
| ~ member(U_3,U_14)
| ~ member(U_4,U_14)
| ~ member(U_5,U_14) )
& ! [U_2,U_1] :
( U_2 = U_1
| ~ apply(U_16,U_1,U_2)
| ~ apply(U_16,U_2,U_1)
| ~ member(U_1,U_14)
| ~ member(U_2,U_14) )
& ! [U_0] :
( apply(U_16,U_0,U_0)
| ~ member(U_0,U_14) ) )
| ~ order(U_16,U_14) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_17,U_15] :
( order(U_17,U_15)
| ? [U_11,U_10,U_9] :
( ~ apply(U_17,U_11,U_9)
& apply(U_17,U_10,U_9)
& apply(U_17,U_11,U_10)
& member(U_9,U_15)
& member(U_10,U_15)
& member(U_11,U_15) )
| ? [U_8,U_7] :
( U_8 != U_7
& apply(U_17,U_7,U_8)
& apply(U_17,U_8,U_7)
& member(U_7,U_15)
& member(U_8,U_15) )
| ( ~ apply(U_17,sK1(U_17,U_15),sK1(U_17,U_15))
& member(sK1(U_17,U_15),U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_5,U_4,U_3] :
( apply(U_16,U_5,U_3)
| ~ apply(U_16,U_4,U_3)
| ~ apply(U_16,U_5,U_4)
| ~ member(U_3,U_14)
| ~ member(U_4,U_14)
| ~ member(U_5,U_14) )
& ! [U_2,U_1] :
( U_2 = U_1
| ~ apply(U_16,U_1,U_2)
| ~ apply(U_16,U_2,U_1)
| ~ member(U_1,U_14)
| ~ member(U_2,U_14) )
& ! [U_0] :
( apply(U_16,U_0,U_0)
| ~ member(U_0,U_14) ) )
| ~ order(U_16,U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1(U_17,U_15))],[f_1_3]) ).
fof(f_1_5,plain,
( ! [U_17,U_15] :
( order(U_17,U_15)
| ? [U_11,U_10,U_9] :
( ~ apply(U_17,U_11,U_9)
& apply(U_17,U_10,U_9)
& apply(U_17,U_11,U_10)
& member(U_9,U_15)
& member(U_10,U_15)
& member(U_11,U_15) )
| ? [U_7] :
( sK2(U_17,U_15) != U_7
& apply(U_17,U_7,sK2(U_17,U_15))
& apply(U_17,sK2(U_17,U_15),U_7)
& member(U_7,U_15)
& member(sK2(U_17,U_15),U_15) )
| ( ~ apply(U_17,sK1(U_17,U_15),sK1(U_17,U_15))
& member(sK1(U_17,U_15),U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_5,U_4,U_3] :
( apply(U_16,U_5,U_3)
| ~ apply(U_16,U_4,U_3)
| ~ apply(U_16,U_5,U_4)
| ~ member(U_3,U_14)
| ~ member(U_4,U_14)
| ~ member(U_5,U_14) )
& ! [U_2,U_1] :
( U_2 = U_1
| ~ apply(U_16,U_1,U_2)
| ~ apply(U_16,U_2,U_1)
| ~ member(U_1,U_14)
| ~ member(U_2,U_14) )
& ! [U_0] :
( apply(U_16,U_0,U_0)
| ~ member(U_0,U_14) ) )
| ~ order(U_16,U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_8,sK2(U_17,U_15))],[f_1_4]) ).
fof(f_1_6,plain,
( ! [U_17,U_15] :
( order(U_17,U_15)
| ? [U_11,U_10,U_9] :
( ~ apply(U_17,U_11,U_9)
& apply(U_17,U_10,U_9)
& apply(U_17,U_11,U_10)
& member(U_9,U_15)
& member(U_10,U_15)
& member(U_11,U_15) )
| ( sK2(U_17,U_15) != sK3(U_17,U_15)
& apply(U_17,sK3(U_17,U_15),sK2(U_17,U_15))
& apply(U_17,sK2(U_17,U_15),sK3(U_17,U_15))
& member(sK3(U_17,U_15),U_15)
& member(sK2(U_17,U_15),U_15) )
| ( ~ apply(U_17,sK1(U_17,U_15),sK1(U_17,U_15))
& member(sK1(U_17,U_15),U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_5,U_4,U_3] :
( apply(U_16,U_5,U_3)
| ~ apply(U_16,U_4,U_3)
| ~ apply(U_16,U_5,U_4)
| ~ member(U_3,U_14)
| ~ member(U_4,U_14)
| ~ member(U_5,U_14) )
& ! [U_2,U_1] :
( U_2 = U_1
| ~ apply(U_16,U_1,U_2)
| ~ apply(U_16,U_2,U_1)
| ~ member(U_1,U_14)
| ~ member(U_2,U_14) )
& ! [U_0] :
( apply(U_16,U_0,U_0)
| ~ member(U_0,U_14) ) )
| ~ order(U_16,U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_7,sK3(U_17,U_15))],[f_1_5]) ).
fof(f_1_7,plain,
( ! [U_17,U_15] :
( order(U_17,U_15)
| ? [U_10,U_9] :
( ~ apply(U_17,sK4(U_17,U_15),U_9)
& apply(U_17,U_10,U_9)
& apply(U_17,sK4(U_17,U_15),U_10)
& member(U_9,U_15)
& member(U_10,U_15)
& member(sK4(U_17,U_15),U_15) )
| ( sK2(U_17,U_15) != sK3(U_17,U_15)
& apply(U_17,sK3(U_17,U_15),sK2(U_17,U_15))
& apply(U_17,sK2(U_17,U_15),sK3(U_17,U_15))
& member(sK3(U_17,U_15),U_15)
& member(sK2(U_17,U_15),U_15) )
| ( ~ apply(U_17,sK1(U_17,U_15),sK1(U_17,U_15))
& member(sK1(U_17,U_15),U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_5,U_4,U_3] :
( apply(U_16,U_5,U_3)
| ~ apply(U_16,U_4,U_3)
| ~ apply(U_16,U_5,U_4)
| ~ member(U_3,U_14)
| ~ member(U_4,U_14)
| ~ member(U_5,U_14) )
& ! [U_2,U_1] :
( U_2 = U_1
| ~ apply(U_16,U_1,U_2)
| ~ apply(U_16,U_2,U_1)
| ~ member(U_1,U_14)
| ~ member(U_2,U_14) )
& ! [U_0] :
( apply(U_16,U_0,U_0)
| ~ member(U_0,U_14) ) )
| ~ order(U_16,U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_11,sK4(U_17,U_15))],[f_1_6]) ).
fof(f_1_8,plain,
( ! [U_17,U_15] :
( order(U_17,U_15)
| ? [U_9] :
( ~ apply(U_17,sK4(U_17,U_15),U_9)
& apply(U_17,sK5(U_17,U_15),U_9)
& apply(U_17,sK4(U_17,U_15),sK5(U_17,U_15))
& member(U_9,U_15)
& member(sK5(U_17,U_15),U_15)
& member(sK4(U_17,U_15),U_15) )
| ( sK2(U_17,U_15) != sK3(U_17,U_15)
& apply(U_17,sK3(U_17,U_15),sK2(U_17,U_15))
& apply(U_17,sK2(U_17,U_15),sK3(U_17,U_15))
& member(sK3(U_17,U_15),U_15)
& member(sK2(U_17,U_15),U_15) )
| ( ~ apply(U_17,sK1(U_17,U_15),sK1(U_17,U_15))
& member(sK1(U_17,U_15),U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_5,U_4,U_3] :
( apply(U_16,U_5,U_3)
| ~ apply(U_16,U_4,U_3)
| ~ apply(U_16,U_5,U_4)
| ~ member(U_3,U_14)
| ~ member(U_4,U_14)
| ~ member(U_5,U_14) )
& ! [U_2,U_1] :
( U_2 = U_1
| ~ apply(U_16,U_1,U_2)
| ~ apply(U_16,U_2,U_1)
| ~ member(U_1,U_14)
| ~ member(U_2,U_14) )
& ! [U_0] :
( apply(U_16,U_0,U_0)
| ~ member(U_0,U_14) ) )
| ~ order(U_16,U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_10,sK5(U_17,U_15))],[f_1_7]) ).
fof(f_1_9,plain,
( ! [U_17,U_15] :
( order(U_17,U_15)
| ( ~ apply(U_17,sK4(U_17,U_15),sK6(U_17,U_15))
& apply(U_17,sK5(U_17,U_15),sK6(U_17,U_15))
& apply(U_17,sK4(U_17,U_15),sK5(U_17,U_15))
& member(sK6(U_17,U_15),U_15)
& member(sK5(U_17,U_15),U_15)
& member(sK4(U_17,U_15),U_15) )
| ( sK2(U_17,U_15) != sK3(U_17,U_15)
& apply(U_17,sK3(U_17,U_15),sK2(U_17,U_15))
& apply(U_17,sK2(U_17,U_15),sK3(U_17,U_15))
& member(sK3(U_17,U_15),U_15)
& member(sK2(U_17,U_15),U_15) )
| ( ~ apply(U_17,sK1(U_17,U_15),sK1(U_17,U_15))
& member(sK1(U_17,U_15),U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_5,U_4,U_3] :
( apply(U_16,U_5,U_3)
| ~ apply(U_16,U_4,U_3)
| ~ apply(U_16,U_5,U_4)
| ~ member(U_3,U_14)
| ~ member(U_4,U_14)
| ~ member(U_5,U_14) )
& ! [U_2,U_1] :
( U_2 = U_1
| ~ apply(U_16,U_1,U_2)
| ~ apply(U_16,U_2,U_1)
| ~ member(U_1,U_14)
| ~ member(U_2,U_14) )
& ! [U_0] :
( apply(U_16,U_0,U_0)
| ~ member(U_0,U_14) ) )
| ~ order(U_16,U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_9,sK6(U_17,U_15))],[f_1_8]) ).
cnf(f_1_11,plain,
( U_2 = U_1
| ~ apply(U_16,U_1,U_2)
| ~ apply(U_16,U_2,U_1)
| ~ member(U_1,U_14)
| ~ member(U_2,U_14)
| ~ order(U_16,U_14) ),
inference(clausify,[status(thm)],[f_1_9]) ).
fof(f_6_1,plain,
! [R,E,M] :
( ( least(M,R,E)
| ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| ~ member(M,E) )
& ( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[least]) ).
fof(f_6_2,plain,
! [U_65,U_64,U_63] :
( ( least(U_63,U_65,U_64)
| ? [U_62] :
( ~ apply(U_65,U_63,U_62)
& member(U_62,U_64) )
| ~ member(U_63,U_64) )
& ( ( ! [U_61] :
( apply(U_65,U_63,U_61)
| ~ member(U_61,U_64) )
& member(U_63,U_64) )
| ~ least(U_63,U_65,U_64) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_71,U_69,U_67] :
( least(U_67,U_71,U_69)
| ? [U_62] :
( ~ apply(U_71,U_67,U_62)
& member(U_62,U_69) )
| ~ member(U_67,U_69) )
& ! [U_70,U_68,U_66] :
( ( ! [U_61] :
( apply(U_70,U_66,U_61)
| ~ member(U_61,U_68) )
& member(U_66,U_68) )
| ~ least(U_66,U_70,U_68) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_71,U_69,U_67] :
( least(U_67,U_71,U_69)
| ( ~ apply(U_71,U_67,sK12(U_71,U_69,U_67))
& member(sK12(U_71,U_69,U_67),U_69) )
| ~ member(U_67,U_69) )
& ! [U_70,U_68,U_66] :
( ( ! [U_61] :
( apply(U_70,U_66,U_61)
| ~ member(U_61,U_68) )
& member(U_66,U_68) )
| ~ least(U_66,U_70,U_68) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_62,sK12(U_71,U_69,U_67))],[f_6_3]) ).
cnf(f_6_5,plain,
( member(U_66,U_68)
| ~ least(U_66,U_70,U_68) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( apply(U_70,U_66,U_61)
| ~ member(U_61,U_68)
| ~ least(U_66,U_70,U_68) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_11_1,negated_conjecture,
~ ! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
inference(negate,[status(cth)],[thIV2]) ).
fof(f_11_2,negated_conjecture,
? [R,E,M] :
( ? [X] :
( M != X
& least(X,R,E) )
& least(M,R,E)
& order(R,E) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_125,U_124,U_123] :
( ? [U_122] :
( U_123 != U_122
& least(U_122,U_125,U_124) )
& least(U_123,U_125,U_124)
& order(U_125,U_124) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_124,U_123] :
( ? [U_122] :
( U_123 != U_122
& least(U_122,sK17,U_124) )
& least(U_123,sK17,U_124)
& order(sK17,U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_125,sK17)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
? [U_123] :
( ? [U_122] :
( U_123 != U_122
& least(U_122,sK17,sK18) )
& least(U_123,sK17,sK18)
& order(sK17,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_124,sK18)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
( ? [U_122] :
( sK19 != U_122
& least(U_122,sK17,sK18) )
& least(sK19,sK17,sK18)
& order(sK17,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_123,sK19)],[f_11_5]) ).
fof(f_11_7,negated_conjecture,
( sK19 != sK20
& least(sK20,sK17,sK18)
& least(sK19,sK17,sK18)
& order(sK17,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_122,sK20)],[f_11_6]) ).
fof(f_11_8,negated_conjecture,
( sK19 != sK20
& least(sK20,sK17,sK18)
& least(sK19,sK17,sK18)
& order(sK17,sK18) ),
inference(definitional_conversion,[status(esa)],[f_11_7]) ).
cnf(f_11_9,negated_conjecture,
order(sK17,sK18),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_10,negated_conjecture,
least(sK19,sK17,sK18),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_11,negated_conjecture,
least(sK20,sK17,sK18),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_12,negated_conjecture,
sK19 != sK20,
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(t1,plain,
sK19 != sK20,
inference(start,[status(thm),parent(0:0)],[f_11_12]) ).
cnf(t2,plain,
( ~ member(sK19,sK18)
| ~ member(sK20,sK18)
| ~ apply(sK17,sK19,sK20)
| ~ apply(sK17,sK20,sK19)
| ~ order(sK17,sK18)
| sK19 = sK20 ),
inference(extension,[status(thm),parent(t1:1)],[f_1_11]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
order(sK17,sK18),
inference(extension,[status(thm),parent(t2:2)],[f_11_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ member(sK19,sK18)
| ~ least(sK20,sK17,sK18)
| apply(sK17,sK20,sK19) ),
inference(extension,[status(thm),parent(t2:3)],[f_6_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
least(sK20,sK17,sK18),
inference(extension,[status(thm),parent(t6:2)],[f_11_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(extension,[status(thm),parent(t6:3)],[f_6_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
least(sK19,sK17,sK18),
inference(extension,[status(thm),parent(t10:2)],[f_11_10]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ member(sK20,sK18)
| ~ least(sK19,sK17,sK18)
| apply(sK17,sK19,sK20) ),
inference(extension,[status(thm),parent(t2:4)],[f_6_6]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:4]) ).
cnf(t16,plain,
least(sK19,sK17,sK18),
inference(extension,[status(thm),parent(t14:2)],[f_11_10]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ least(sK20,sK17,sK18)
| member(sK20,sK18) ),
inference(extension,[status(thm),parent(t14:3)],[f_6_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
least(sK20,sK17,sK18),
inference(extension,[status(thm),parent(t18:2)],[f_11_11]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ least(sK20,sK17,sK18)
| member(sK20,sK18) ),
inference(extension,[status(thm),parent(t2:5)],[f_6_5]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:5]) ).
cnf(t24,plain,
least(sK20,sK17,sK18),
inference(extension,[status(thm),parent(t22:2)],[f_11_11]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(extension,[status(thm),parent(t2:6)],[f_6_5]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t2:6]) ).
cnf(t28,plain,
least(sK19,sK17,sK18),
inference(extension,[status(thm),parent(t26:2)],[f_11_10]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.36 % Computer : n010.cluster.edu
% 0.11/10.36 % Model : x86_64 x86_64
% 0.11/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.36 % Memory : 8046.5625MB
% 0.11/10.36 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Sat Sep 19 22:58:23 UTC 2026
% 0.11/10.37 % CPUTime :
% 0.14/10.88 % SZS status Theorem for theBenchmark
% 0.14/10.88 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------