%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:57:09 AM UTC 2026
% Result : Theorem 67.79s 68.14s
% Output : Proof 67.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 117 ( 41 unt; 0 def)
% Number of atoms : 295 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 308 ( 130 ~; 120 |; 53 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 122 ( 2 sgn 68 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('theBenchmark.p',union_defn) ).
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(prove_intersect_with_union,conjecture,
! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,D)
| intersect(B,C) ) ),
file('theBenchmark.p',prove_intersect_with_union) ).
fof(f_1_1,plain,
! [B,C,D] :
( ( member(D,union(B,C))
| ( ~ member(D,C)
& ~ member(D,B) ) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(fof_nnf,[status(thm)],[union_defn]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( ( member(U_0,union(U_2,U_1))
| ( ~ member(U_0,U_1)
& ~ member(U_0,U_2) ) )
& ( member(U_0,U_1)
| member(U_0,U_2)
| ~ member(U_0,union(U_2,U_1)) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_8,U_6,U_4] :
( member(U_4,union(U_8,U_6))
| ( ~ member(U_4,U_6)
& ~ member(U_4,U_8) ) )
& ! [U_7,U_5,U_3] :
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_8,U_4,U_6] :
( ~ member(U_4,U_6)
| ~ sP0(U_8,U_4,U_6) )
& ! [U_8,U_4,U_6] :
( ~ member(U_4,U_8)
| ~ sP0(U_8,U_4,U_6) )
& ! [U_8,U_4,U_6] :
( member(U_4,union(U_8,U_6))
| sP0(U_8,U_4,U_6) )
& ! [U_7,U_5,U_3] :
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_3,U_5)
| member(U_3,U_7)
| ~ member(U_3,union(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( member(U_4,union(U_8,U_6))
| sP0(U_8,U_4,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ member(U_4,U_8)
| ~ sP0(U_8,U_4,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_8,plain,
( ~ member(U_4,U_6)
| ~ sP0(U_8,U_4,U_6) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [B,C] :
( ( intersect(B,C)
| ! [D] :
( ~ member(D,C)
| ~ member(D,B) ) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(f_2_2,plain,
! [U_12,U_11] :
( ( intersect(U_12,U_11)
| ! [U_10] :
( ~ member(U_10,U_11)
| ~ member(U_10,U_12) ) )
& ( ? [U_9] :
( member(U_9,U_11)
& member(U_9,U_12) )
| ~ intersect(U_12,U_11) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_16,U_14] :
( intersect(U_16,U_14)
| ! [U_10] :
( ~ member(U_10,U_14)
| ~ member(U_10,U_16) ) )
& ! [U_15,U_13] :
( ? [U_9] :
( member(U_9,U_13)
& member(U_9,U_15) )
| ~ intersect(U_15,U_13) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_16,U_14] :
( intersect(U_16,U_14)
| ! [U_10] :
( ~ member(U_10,U_14)
| ~ member(U_10,U_16) ) )
& ! [U_15,U_13] :
( ( member(sK1(U_15,U_13),U_13)
& member(sK1(U_15,U_13),U_15) )
| ~ intersect(U_15,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1(U_15,U_13))],[f_2_3]) ).
fof(f_2_5,plain,
( ! [U_15,U_13] :
( member(sK1(U_15,U_13),U_13)
| ~ sP1(U_15,U_13) )
& ! [U_15,U_13] :
( member(sK1(U_15,U_13),U_15)
| ~ sP1(U_15,U_13) )
& ! [U_14,U_16,U_10] :
( intersect(U_16,U_14)
| ~ member(U_10,U_14)
| ~ member(U_10,U_16) )
& ! [U_15,U_13] :
( sP1(U_15,U_13)
| ~ intersect(U_15,U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_2_4]) ).
cnf(f_2_6,plain,
( sP1(U_15,U_13)
| ~ intersect(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_7,plain,
( intersect(U_16,U_14)
| ~ member(U_10,U_14)
| ~ member(U_10,U_16) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_8,plain,
( member(sK1(U_15,U_13),U_15)
| ~ sP1(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_9,plain,
( member(sK1(U_15,U_13),U_13)
| ~ sP1(U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
fof(f_4_1,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(fof_nnf,[status(thm)],[symmetry_of_intersect]) ).
fof(f_4_2,plain,
! [U_20,U_19] :
( intersect(U_19,U_20)
| ~ intersect(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_20,U_19] :
( intersect(U_19,U_20)
| ~ intersect(U_20,U_19) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( intersect(U_19,U_20)
| ~ intersect(U_20,U_19) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_6_1,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,D)
| intersect(B,C) ) ),
inference(negate,[status(cth)],[prove_intersect_with_union]) ).
fof(f_6_2,negated_conjecture,
? [B,C,D] :
( ( ~ intersect(B,union(C,D))
& ( intersect(B,D)
| intersect(B,C) ) )
| ( ~ intersect(B,D)
& ~ intersect(B,C)
& intersect(B,union(C,D)) ) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_35,U_34,U_33] :
( ( ~ intersect(U_35,union(U_34,U_33))
& ( intersect(U_35,U_33)
| intersect(U_35,U_34) ) )
| ( ~ intersect(U_35,U_33)
& ~ intersect(U_35,U_34)
& intersect(U_35,union(U_34,U_33)) ) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
( ? [U_41,U_39,U_37] :
( ~ intersect(U_41,union(U_39,U_37))
& ( intersect(U_41,U_37)
| intersect(U_41,U_39) ) )
| ? [U_40,U_38,U_36] :
( ~ intersect(U_40,U_36)
& ~ intersect(U_40,U_38)
& intersect(U_40,union(U_38,U_36)) ) ),
inference(miniscope,[status(thm)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
( ? [U_41,U_39,U_37] :
( ~ intersect(U_41,union(U_39,U_37))
& ( intersect(U_41,U_37)
| intersect(U_41,U_39) ) )
| ? [U_38,U_36] :
( ~ intersect(sK4,U_36)
& ~ intersect(sK4,U_38)
& intersect(sK4,union(U_38,U_36)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_40,sK4)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( ? [U_41,U_39,U_37] :
( ~ intersect(U_41,union(U_39,U_37))
& ( intersect(U_41,U_37)
| intersect(U_41,U_39) ) )
| ? [U_36] :
( ~ intersect(sK4,U_36)
& ~ intersect(sK4,sK5)
& intersect(sK4,union(sK5,U_36)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_38,sK5)],[f_6_5]) ).
fof(f_6_7,negated_conjecture,
( ? [U_41,U_39,U_37] :
( ~ intersect(U_41,union(U_39,U_37))
& ( intersect(U_41,U_37)
| intersect(U_41,U_39) ) )
| ( ~ intersect(sK4,sK6)
& ~ intersect(sK4,sK5)
& intersect(sK4,union(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_36,sK6)],[f_6_6]) ).
fof(f_6_8,negated_conjecture,
( ? [U_39,U_37] :
( ~ intersect(sK7,union(U_39,U_37))
& ( intersect(sK7,U_37)
| intersect(sK7,U_39) ) )
| ( ~ intersect(sK4,sK6)
& ~ intersect(sK4,sK5)
& intersect(sK4,union(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7)],[f_6_7]) ).
fof(f_6_9,negated_conjecture,
( ? [U_37] :
( ~ intersect(sK7,union(sK8,U_37))
& ( intersect(sK7,U_37)
| intersect(sK7,sK8) ) )
| ( ~ intersect(sK4,sK6)
& ~ intersect(sK4,sK5)
& intersect(sK4,union(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_39,sK8)],[f_6_8]) ).
fof(f_6_10,negated_conjecture,
( ( ~ intersect(sK7,union(sK8,sK9))
& ( intersect(sK7,sK9)
| intersect(sK7,sK8) ) )
| ( ~ intersect(sK4,sK6)
& ~ intersect(sK4,sK5)
& intersect(sK4,union(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_37,sK9)],[f_6_9]) ).
fof(f_6_11,negated_conjecture,
( ( ~ intersect(sK7,union(sK8,sK9))
| ~ sP6 )
& ( intersect(sK7,sK9)
| intersect(sK7,sK8)
| ~ sP6 )
& ( ~ intersect(sK4,sK6)
| ~ sP5 )
& ( ~ intersect(sK4,sK5)
| ~ sP5 )
& ( intersect(sK4,union(sK5,sK6))
| ~ sP5 )
& ( sP6
| sP5 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6])],[f_6_10]) ).
cnf(f_6_12,negated_conjecture,
( sP6
| sP5 ),
inference(clausify,[status(thm)],[f_6_11]) ).
cnf(f_6_13,negated_conjecture,
( intersect(sK4,union(sK5,sK6))
| ~ sP5 ),
inference(clausify,[status(thm)],[f_6_11]) ).
cnf(f_6_14,negated_conjecture,
( ~ intersect(sK4,sK5)
| ~ sP5 ),
inference(clausify,[status(thm)],[f_6_11]) ).
cnf(f_6_15,negated_conjecture,
( ~ intersect(sK4,sK6)
| ~ sP5 ),
inference(clausify,[status(thm)],[f_6_11]) ).
cnf(f_6_16,negated_conjecture,
( intersect(sK7,sK9)
| intersect(sK7,sK8)
| ~ sP6 ),
inference(clausify,[status(thm)],[f_6_11]) ).
cnf(f_6_17,negated_conjecture,
( ~ intersect(sK7,union(sK8,sK9))
| ~ sP6 ),
inference(clausify,[status(thm)],[f_6_11]) ).
cnf(t1,plain,
( sP6
| sP5 ),
inference(start,[status(thm),parent(0:0)],[f_6_12]) ).
cnf(t2,plain,
( ~ intersect(sK4,sK6)
| ~ sP5 ),
inference(extension,[status(thm),parent(t1:1)],[f_6_15]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ intersect(sK6,sK4)
| intersect(sK4,sK6) ),
inference(extension,[status(thm),parent(t2:2)],[f_4_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ member(sK1(sK4,union(sK5,sK6)),sK4)
| ~ member(sK1(sK4,union(sK5,sK6)),sK6)
| intersect(sK6,sK4) ),
inference(extension,[status(thm),parent(t4:2)],[f_2_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( member(sK1(sK4,union(sK5,sK6)),sK5)
| ~ member(sK1(sK4,union(sK5,sK6)),union(sK5,sK6))
| member(sK1(sK4,union(sK5,sK6)),sK6) ),
inference(extension,[status(thm),parent(t6:2)],[f_1_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ sP1(sK4,union(sK5,sK6))
| member(sK1(sK4,union(sK5,sK6)),union(sK5,sK6)) ),
inference(extension,[status(thm),parent(t8:2)],[f_2_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ intersect(sK4,union(sK5,sK6))
| sP1(sK4,union(sK5,sK6)) ),
inference(extension,[status(thm),parent(t10:2)],[f_2_6]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ sP5
| intersect(sK4,union(sK5,sK6)) ),
inference(extension,[status(thm),parent(t12:2)],[f_6_13]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
$false,
inference(reduction,[status(thm),parent(t14:2)],[t14:2,t1:1]) ).
cnf(t17,plain,
( ~ member(sK1(sK4,union(sK5,sK6)),sK4)
| intersect(sK5,sK4)
| ~ member(sK1(sK4,union(sK5,sK6)),sK5) ),
inference(extension,[status(thm),parent(t8:3)],[f_2_7]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t8:3]) ).
cnf(t19,plain,
( intersect(sK4,sK5)
| ~ intersect(sK5,sK4) ),
inference(extension,[status(thm),parent(t17:2)],[f_4_4]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
( ~ sP5
| ~ intersect(sK4,sK5) ),
inference(extension,[status(thm),parent(t19:2)],[f_6_14]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
$false,
inference(reduction,[status(thm),parent(t21:2)],[t21:2,t1:1]) ).
cnf(t24,plain,
( ~ sP1(sK4,union(sK5,sK6))
| member(sK1(sK4,union(sK5,sK6)),sK4) ),
inference(extension,[status(thm),parent(t17:3)],[f_2_8]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t17:3]) ).
cnf(t26,plain,
( ~ intersect(sK4,union(sK5,sK6))
| sP1(sK4,union(sK5,sK6)) ),
inference(extension,[status(thm),parent(t24:2)],[f_2_6]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ sP5
| intersect(sK4,union(sK5,sK6)) ),
inference(extension,[status(thm),parent(t26:2)],[f_6_13]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
$false,
inference(reduction,[status(thm),parent(t28:2)],[t28:2,t1:1]) ).
cnf(t31,plain,
( ~ sP1(sK4,union(sK5,sK6))
| member(sK1(sK4,union(sK5,sK6)),sK4) ),
inference(extension,[status(thm),parent(t6:3)],[f_2_8]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t6:3]) ).
cnf(t33,plain,
( ~ intersect(sK4,union(sK5,sK6))
| sP1(sK4,union(sK5,sK6)) ),
inference(extension,[status(thm),parent(t31:2)],[f_2_6]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t31:2]) ).
cnf(t35,plain,
( ~ sP5
| intersect(sK4,union(sK5,sK6)) ),
inference(extension,[status(thm),parent(t33:2)],[f_6_13]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t33:2]) ).
cnf(t37,plain,
$false,
inference(reduction,[status(thm),parent(t35:2)],[t35:2,t1:1]) ).
cnf(t38,plain,
( intersect(sK7,sK8)
| intersect(sK7,sK9)
| ~ sP6 ),
inference(extension,[status(thm),parent(t1:2)],[f_6_16]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t1:2]) ).
cnf(t40,plain,
( sP1(sK7,sK9)
| ~ intersect(sK7,sK9) ),
inference(extension,[status(thm),parent(t38:2)],[f_2_6]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
( member(sK1(sK7,sK9),sK9)
| ~ sP1(sK7,sK9) ),
inference(extension,[status(thm),parent(t40:2)],[f_2_9]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( ~ sP0(sK8,sK1(sK7,sK9),sK9)
| ~ member(sK1(sK7,sK9),sK9) ),
inference(extension,[status(thm),parent(t42:2)],[f_1_8]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( member(sK1(sK7,sK9),union(sK8,sK9))
| sP0(sK8,sK1(sK7,sK9),sK9) ),
inference(extension,[status(thm),parent(t44:2)],[f_1_6]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
( ~ member(sK1(sK7,sK9),sK7)
| intersect(union(sK8,sK9),sK7)
| ~ member(sK1(sK7,sK9),union(sK8,sK9)) ),
inference(extension,[status(thm),parent(t46:2)],[f_2_7]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
( intersect(sK7,union(sK8,sK9))
| ~ intersect(union(sK8,sK9),sK7) ),
inference(extension,[status(thm),parent(t48:2)],[f_4_4]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( ~ sP6
| ~ intersect(sK7,union(sK8,sK9)) ),
inference(extension,[status(thm),parent(t50:2)],[f_6_17]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
$false,
inference(reduction,[status(thm),parent(t52:2)],[t52:2,t1:2]) ).
cnf(t55,plain,
( ~ sP1(sK7,sK9)
| member(sK1(sK7,sK9),sK7) ),
inference(extension,[status(thm),parent(t48:3)],[f_2_8]) ).
cnf(t56,plain,
$false,
inference(connection,[status(thm),parent(t55:1)],[t55:1,t48:3]) ).
cnf(t57,plain,
$false,
inference(reduction,[status(thm),parent(t55:2)],[t55:2,t40:2]) ).
cnf(t58,plain,
( sP1(sK7,sK8)
| ~ intersect(sK7,sK8) ),
inference(extension,[status(thm),parent(t38:3)],[f_2_6]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t38:3]) ).
cnf(t60,plain,
( member(sK1(sK7,sK8),sK8)
| ~ sP1(sK7,sK8) ),
inference(extension,[status(thm),parent(t58:2)],[f_2_9]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
( ~ sP0(sK8,sK1(sK7,sK8),sK9)
| ~ member(sK1(sK7,sK8),sK8) ),
inference(extension,[status(thm),parent(t60:2)],[f_1_7]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( member(sK1(sK7,sK8),union(sK8,sK9))
| sP0(sK8,sK1(sK7,sK8),sK9) ),
inference(extension,[status(thm),parent(t62:2)],[f_1_6]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
( ~ member(sK1(sK7,sK8),sK7)
| intersect(union(sK8,sK9),sK7)
| ~ member(sK1(sK7,sK8),union(sK8,sK9)) ),
inference(extension,[status(thm),parent(t64:2)],[f_2_7]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
( intersect(sK7,union(sK8,sK9))
| ~ intersect(union(sK8,sK9),sK7) ),
inference(extension,[status(thm),parent(t66:2)],[f_4_4]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
( ~ sP6
| ~ intersect(sK7,union(sK8,sK9)) ),
inference(extension,[status(thm),parent(t68:2)],[f_6_17]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
$false,
inference(reduction,[status(thm),parent(t70:2)],[t70:2,t1:2]) ).
cnf(t73,plain,
( ~ sP1(sK7,sK8)
| member(sK1(sK7,sK8),sK7) ),
inference(extension,[status(thm),parent(t66:3)],[f_2_8]) ).
cnf(t74,plain,
$false,
inference(connection,[status(thm),parent(t73:1)],[t73:1,t66:3]) ).
cnf(t75,plain,
$false,
inference(reduction,[status(thm),parent(t73:2)],[t73:2,t58:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 22:44:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 67.79/68.14 % SZS status Theorem for theBenchmark
% 67.79/68.14 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------