%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET633+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n018.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 08:57:11 AM UTC 2026
% Result : Theorem 57.65s 57.96s
% Output : Proof 57.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 97 ( 43 unt; 0 def)
% Number of atoms : 259 ( 40 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 273 ( 111 ~; 102 |; 53 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 171 ( 5 sgn 111 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('theBenchmark.p',symmetric_difference_defn) ).
fof(union_subset,axiom,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('theBenchmark.p',union_subset) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(commutativity_of_symmetric_difference,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_th115,conjecture,
! [B,C,D] :
( ( subset(difference(C,B),D)
& subset(difference(B,C),D) )
=> subset(symmetric_difference(B,C),D) ),
file('theBenchmark.p',prove_th115) ).
fof(f_1_1,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(fof_nnf,[status(thm)],[symmetric_difference_defn]) ).
fof(f_1_2,plain,
! [U_1,U_0] : symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] : symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [B,C,D] :
( subset(union(B,D),C)
| ~ subset(D,C)
| ~ subset(B,C) ),
inference(fof_nnf,[status(thm)],[union_subset]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] :
( subset(union(U_4,U_2),U_3)
| ~ subset(U_2,U_3)
| ~ subset(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2,U_3,U_4] :
( subset(union(U_4,U_2),U_3)
| ~ subset(U_2,U_3)
| ~ subset(U_4,U_3) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(union(U_4,U_2),U_3)
| ~ subset(U_2,U_3)
| ~ subset(U_4,U_3) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_4_1,plain,
! [B,C] :
( ( subset(B,C)
| ? [D] :
( ~ member(D,C)
& member(D,B) ) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(f_4_2,plain,
! [U_17,U_16] :
( ( subset(U_17,U_16)
| ? [U_15] :
( ~ member(U_15,U_16)
& member(U_15,U_17) ) )
& ( ! [U_14] :
( member(U_14,U_16)
| ~ member(U_14,U_17) )
| ~ subset(U_17,U_16) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_21,U_19] :
( subset(U_21,U_19)
| ? [U_15] :
( ~ member(U_15,U_19)
& member(U_15,U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( member(U_14,U_18)
| ~ member(U_14,U_20) )
| ~ subset(U_20,U_18) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_21,U_19] :
( subset(U_21,U_19)
| ( ~ member(sK1(U_21,U_19),U_19)
& member(sK1(U_21,U_19),U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( member(U_14,U_18)
| ~ member(U_14,U_20) )
| ~ subset(U_20,U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1(U_21,U_19))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_21,U_19] :
( ~ member(sK1(U_21,U_19),U_19)
| ~ sP1(U_21,U_19) )
& ! [U_21,U_19] :
( member(sK1(U_21,U_19),U_21)
| ~ sP1(U_21,U_19) )
& ! [U_21,U_19] :
( subset(U_21,U_19)
| sP1(U_21,U_19) )
& ! [U_20,U_14,U_18] :
( member(U_14,U_18)
| ~ member(U_14,U_20)
| ~ subset(U_20,U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_4_4]) ).
cnf(f_4_6,plain,
( member(U_14,U_18)
| ~ member(U_14,U_20)
| ~ subset(U_20,U_18) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( subset(U_21,U_19)
| sP1(U_21,U_19) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( member(sK1(U_21,U_19),U_21)
| ~ sP1(U_21,U_19) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( ~ member(sK1(U_21,U_19),U_19)
| ~ sP1(U_21,U_19) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_6_1,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_symmetric_difference]) ).
fof(f_6_2,plain,
! [U_25,U_24] : symmetric_difference(U_25,U_24) = symmetric_difference(U_24,U_25),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_24,U_25] : symmetric_difference(U_25,U_24) = symmetric_difference(U_24,U_25),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
symmetric_difference(U_25,U_24) = symmetric_difference(U_24,U_25),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [B,C] :
( ( B = C
| ? [D] :
( ( ~ member(D,B)
& member(D,C) )
| ( ~ member(D,C)
& member(D,B) ) ) )
& ( ! [D] :
( ( member(D,B)
| ~ member(D,C) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(fof_nnf,[status(thm)],[equal_member_defn]) ).
fof(f_7_2,plain,
! [U_29,U_28] :
( ( U_29 = U_28
| ? [U_27] :
( ( ~ member(U_27,U_29)
& member(U_27,U_28) )
| ( ~ member(U_27,U_28)
& member(U_27,U_29) ) ) )
& ( ! [U_26] :
( ( member(U_26,U_29)
| ~ member(U_26,U_28) )
& ( member(U_26,U_28)
| ~ member(U_26,U_29) ) )
| U_29 != U_28 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ? [U_33] :
( ~ member(U_33,U_37)
& member(U_33,U_35) )
| ? [U_32] :
( ~ member(U_32,U_35)
& member(U_32,U_37) ) )
& ! [U_36,U_34] :
( ( ! [U_31] :
( member(U_31,U_36)
| ~ member(U_31,U_34) )
& ! [U_30] :
( member(U_30,U_34)
| ~ member(U_30,U_36) ) )
| U_36 != U_34 ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ? [U_33] :
( ~ member(U_33,U_37)
& member(U_33,U_35) )
| ( ~ member(sK2(U_37,U_35),U_35)
& member(sK2(U_37,U_35),U_37) ) )
& ! [U_36,U_34] :
( ( ! [U_31] :
( member(U_31,U_36)
| ~ member(U_31,U_34) )
& ! [U_30] :
( member(U_30,U_34)
| ~ member(U_30,U_36) ) )
| U_36 != U_34 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_32,sK2(U_37,U_35))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ( ~ member(sK3(U_37,U_35),U_37)
& member(sK3(U_37,U_35),U_35) )
| ( ~ member(sK2(U_37,U_35),U_35)
& member(sK2(U_37,U_35),U_37) ) )
& ! [U_36,U_34] :
( ( ! [U_31] :
( member(U_31,U_36)
| ~ member(U_31,U_34) )
& ! [U_30] :
( member(U_30,U_34)
| ~ member(U_30,U_36) ) )
| U_36 != U_34 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_33,sK3(U_37,U_35))],[f_7_4]) ).
fof(f_7_6,plain,
( ! [U_37,U_35] :
( ~ member(sK3(U_37,U_35),U_37)
| ~ sP4(U_37,U_35) )
& ! [U_37,U_35] :
( member(sK3(U_37,U_35),U_35)
| ~ sP4(U_37,U_35) )
& ! [U_37,U_35] :
( ~ member(sK2(U_37,U_35),U_35)
| ~ sP3(U_37,U_35) )
& ! [U_37,U_35] :
( member(sK2(U_37,U_35),U_37)
| ~ sP3(U_37,U_35) )
& ! [U_30,U_31,U_36,U_34] :
( member(U_31,U_36)
| ~ member(U_31,U_34)
| ~ sP2(U_30,U_31,U_36,U_34) )
& ! [U_30,U_31,U_36,U_34] :
( member(U_30,U_34)
| ~ member(U_30,U_36)
| ~ sP2(U_30,U_31,U_36,U_34) )
& ! [U_37,U_35] :
( U_37 = U_35
| sP4(U_37,U_35)
| sP3(U_37,U_35) )
& ! [U_30,U_31,U_36,U_34] :
( sP2(U_30,U_31,U_36,U_34)
| U_36 != U_34 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3,sP4])],[f_7_5]) ).
cnf(f_7_7,plain,
( sP2(U_30,U_31,U_36,U_34)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_8,plain,
( U_37 = U_35
| sP4(U_37,U_35)
| sP3(U_37,U_35) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_10,plain,
( member(U_31,U_36)
| ~ member(U_31,U_34)
| ~ sP2(U_30,U_31,U_36,U_34) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_11,plain,
( member(sK2(U_37,U_35),U_37)
| ~ sP3(U_37,U_35) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_12,plain,
( ~ member(sK2(U_37,U_35),U_35)
| ~ sP3(U_37,U_35) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_13,plain,
( member(sK3(U_37,U_35),U_35)
| ~ sP4(U_37,U_35) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_14,plain,
( ~ member(sK3(U_37,U_35),U_37)
| ~ sP4(U_37,U_35) ),
inference(clausify,[status(thm)],[f_7_6]) ).
fof(f_9_1,negated_conjecture,
~ ! [B,C,D] :
( ( subset(difference(C,B),D)
& subset(difference(B,C),D) )
=> subset(symmetric_difference(B,C),D) ),
inference(negate,[status(cth)],[prove_th115]) ).
fof(f_9_2,negated_conjecture,
? [B,C,D] :
( ~ subset(symmetric_difference(B,C),D)
& subset(difference(C,B),D)
& subset(difference(B,C),D) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_41,U_40,U_39] :
( ~ subset(symmetric_difference(U_41,U_40),U_39)
& subset(difference(U_40,U_41),U_39)
& subset(difference(U_41,U_40),U_39) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_40,U_39] :
( ~ subset(symmetric_difference(sK4,U_40),U_39)
& subset(difference(U_40,sK4),U_39)
& subset(difference(sK4,U_40),U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_41,sK4)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
? [U_39] :
( ~ subset(symmetric_difference(sK4,sK5),U_39)
& subset(difference(sK5,sK4),U_39)
& subset(difference(sK4,sK5),U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_40,sK5)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ~ subset(symmetric_difference(sK4,sK5),sK6)
& subset(difference(sK5,sK4),sK6)
& subset(difference(sK4,sK5),sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_39,sK6)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ~ subset(symmetric_difference(sK4,sK5),sK6)
& subset(difference(sK5,sK4),sK6)
& subset(difference(sK4,sK5),sK6) ),
inference(definitional_conversion,[status(esa)],[f_9_6]) ).
cnf(f_9_8,negated_conjecture,
subset(difference(sK4,sK5),sK6),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,negated_conjecture,
subset(difference(sK5,sK4),sK6),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_10,negated_conjecture,
~ subset(symmetric_difference(sK4,sK5),sK6),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_11,axiom,
( member(Eq_y_0,Eq_y_1)
| ~ member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
subset(difference(sK4,sK5),sK6),
inference(start,[status(thm),parent(0:0)],[f_9_8]) ).
cnf(t2,plain,
( ~ subset(difference(sK5,sK4),sK6)
| subset(union(difference(sK4,sK5),difference(sK5,sK4)),sK6)
| ~ subset(difference(sK4,sK5),sK6) ),
inference(extension,[status(thm),parent(t1:1)],[f_2_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(sK1(symmetric_difference(sK4,sK5),sK6),union(difference(sK4,sK5),difference(sK5,sK4)))
| member(sK1(symmetric_difference(sK4,sK5),sK6),sK6)
| ~ subset(union(difference(sK4,sK5),difference(sK5,sK4)),sK6) ),
inference(extension,[status(thm),parent(t2:2)],[f_4_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ sP1(symmetric_difference(sK4,sK5),sK6)
| ~ member(sK1(symmetric_difference(sK4,sK5),sK6),sK6) ),
inference(extension,[status(thm),parent(t4:2)],[f_4_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( subset(symmetric_difference(sK4,sK5),sK6)
| sP1(symmetric_difference(sK4,sK5),sK6) ),
inference(extension,[status(thm),parent(t6:2)],[f_4_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
~ subset(symmetric_difference(sK4,sK5),sK6),
inference(extension,[status(thm),parent(t8:2)],[f_9_10]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( symmetric_difference(sK5,sK4) != union(difference(sK4,sK5),difference(sK5,sK4))
| ~ member(sK1(symmetric_difference(sK4,sK5),sK6),symmetric_difference(sK5,sK4))
| sK1(symmetric_difference(sK4,sK5),sK6) != sK1(symmetric_difference(sK4,sK5),sK6)
| member(sK1(symmetric_difference(sK4,sK5),sK6),union(difference(sK4,sK5),difference(sK5,sK4))) ),
inference(extension,[status(thm),parent(t4:3)],[equality_11]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
( sP4(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6))
| sP3(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6))
| sK1(symmetric_difference(sK4,sK5),sK6) = sK1(symmetric_difference(sK4,sK5),sK6) ),
inference(extension,[status(thm),parent(t12:2)],[f_7_8]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ member(sK2(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6)),sK1(symmetric_difference(sK4,sK5),sK6))
| ~ sP3(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6)) ),
inference(extension,[status(thm),parent(t14:2)],[f_7_12]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ sP3(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6))
| member(sK2(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6)),sK1(symmetric_difference(sK4,sK5),sK6)) ),
inference(extension,[status(thm),parent(t16:2)],[f_7_11]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
$false,
inference(reduction,[status(thm),parent(t18:2)],[t18:2,t14:2]) ).
cnf(t21,plain,
( ~ member(sK3(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6)),sK1(symmetric_difference(sK4,sK5),sK6))
| ~ sP4(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6)) ),
inference(extension,[status(thm),parent(t14:3)],[f_7_14]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t14:3]) ).
cnf(t23,plain,
( ~ sP4(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6))
| member(sK3(sK1(symmetric_difference(sK4,sK5),sK6),sK1(symmetric_difference(sK4,sK5),sK6)),sK1(symmetric_difference(sK4,sK5),sK6)) ),
inference(extension,[status(thm),parent(t21:2)],[f_7_13]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t21:2]) ).
cnf(t25,plain,
$false,
inference(reduction,[status(thm),parent(t23:2)],[t23:2,t14:3]) ).
cnf(t26,plain,
( ~ member(sK1(symmetric_difference(sK4,sK5),sK6),symmetric_difference(sK4,sK5))
| ~ sP2(U_704,sK1(symmetric_difference(sK4,sK5),sK6),symmetric_difference(sK5,sK4),symmetric_difference(sK4,sK5))
| member(sK1(symmetric_difference(sK4,sK5),sK6),symmetric_difference(sK5,sK4)) ),
inference(extension,[status(thm),parent(t12:3)],[f_7_10]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t12:3]) ).
cnf(t28,plain,
( symmetric_difference(sK5,sK4) != symmetric_difference(sK4,sK5)
| sP2(U_704,sK1(symmetric_difference(sK4,sK5),sK6),symmetric_difference(sK5,sK4),symmetric_difference(sK4,sK5)) ),
inference(extension,[status(thm),parent(t26:2)],[f_7_7]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
symmetric_difference(sK5,sK4) = symmetric_difference(sK4,sK5),
inference(extension,[status(thm),parent(t28:2)],[f_6_4]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( ~ sP1(symmetric_difference(sK4,sK5),sK6)
| member(sK1(symmetric_difference(sK4,sK5),sK6),symmetric_difference(sK4,sK5)) ),
inference(extension,[status(thm),parent(t26:3)],[f_4_8]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:3]) ).
cnf(t34,plain,
( subset(symmetric_difference(sK4,sK5),sK6)
| sP1(symmetric_difference(sK4,sK5),sK6) ),
inference(extension,[status(thm),parent(t32:2)],[f_4_7]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
~ subset(symmetric_difference(sK4,sK5),sK6),
inference(extension,[status(thm),parent(t34:2)],[f_9_10]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( symmetric_difference(sK4,sK5) != union(difference(sK4,sK5),difference(sK5,sK4))
| symmetric_difference(sK5,sK4) != symmetric_difference(sK4,sK5)
| symmetric_difference(sK5,sK4) = union(difference(sK4,sK5),difference(sK5,sK4)) ),
inference(extension,[status(thm),parent(t12:4)],[equality_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t12:4]) ).
cnf(t40,plain,
symmetric_difference(sK5,sK4) = symmetric_difference(sK4,sK5),
inference(extension,[status(thm),parent(t38:2)],[f_6_4]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
symmetric_difference(sK4,sK5) = union(difference(sK4,sK5),difference(sK5,sK4)),
inference(extension,[status(thm),parent(t38:3)],[f_1_4]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t38:3]) ).
cnf(t44,plain,
subset(difference(sK5,sK4),sK6),
inference(extension,[status(thm),parent(t2:3)],[f_9_9]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET633+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 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
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 22:46:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 57.65/57.96 % SZS status Theorem for theBenchmark
% 57.65/57.96 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------