%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n005.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 08:58:46 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 90 ( 35 unt; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 159 ( 66 ~; 56 |; 25 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 134 ( 6 sgn 96 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(d1_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
<=> subset(C,cartesian_product2(A,B)) ),
file('theBenchmark.p',d1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t119_zfmisc_1,axiom,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) ) ),
file('theBenchmark.p',t12_relset_1) ).
fof(t14_relset_1,conjecture,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
file('theBenchmark.p',t14_relset_1) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t21_relat_1,axiom,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_1) ).
fof(f_1_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( relation(U_0)
| ~ element(U_0,powerset(cartesian_product2(U_2,U_1))) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( relation(U_0)
| ~ element(U_0,powerset(cartesian_product2(U_2,U_1))) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B,C] :
( ( relation_of2(C,A,B)
| ~ subset(C,cartesian_product2(A,B)) )
& ( subset(C,cartesian_product2(A,B))
| ~ relation_of2(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[d1_relset_1]) ).
fof(f_2_2,plain,
! [U_5,U_4,U_3] :
( ( relation_of2(U_3,U_5,U_4)
| ~ subset(U_3,cartesian_product2(U_5,U_4)) )
& ( subset(U_3,cartesian_product2(U_5,U_4))
| ~ relation_of2(U_3,U_5,U_4) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_11,U_9,U_7] :
( relation_of2(U_7,U_11,U_9)
| ~ subset(U_7,cartesian_product2(U_11,U_9)) )
& ! [U_10,U_8,U_6] :
( subset(U_6,cartesian_product2(U_10,U_8))
| ~ relation_of2(U_6,U_10,U_8) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_5,plain,
( relation_of2(U_7,U_11,U_9)
| ~ subset(U_7,cartesian_product2(U_11,U_9)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_9_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_9_2,plain,
! [U_14,U_13,U_12] :
( element(U_12,powerset(cartesian_product2(U_14,U_13)))
| ~ relation_of2_as_subset(U_12,U_14,U_13) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( element(U_12,powerset(cartesian_product2(U_14,U_13)))
| ~ relation_of2_as_subset(U_12,U_14,U_13) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_13_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_13_2,plain,
! [U_25,U_24,U_23] :
( ( relation_of2_as_subset(U_23,U_25,U_24)
| ~ relation_of2(U_23,U_25,U_24) )
& ( relation_of2(U_23,U_25,U_24)
| ~ relation_of2_as_subset(U_23,U_25,U_24) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_31,U_29,U_27] :
( relation_of2_as_subset(U_27,U_31,U_29)
| ~ relation_of2(U_27,U_31,U_29) )
& ! [U_30,U_28,U_26] :
( relation_of2(U_26,U_30,U_28)
| ~ relation_of2_as_subset(U_26,U_30,U_28) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_5,plain,
( relation_of2_as_subset(U_27,U_31,U_29)
| ~ relation_of2(U_27,U_31,U_29) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_14_2,plain,
! [U_33,U_32] : subset(U_33,U_33),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_33] : subset(U_33,U_33),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
subset(U_33,U_33),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B,C,D] :
( subset(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t119_zfmisc_1]) ).
fof(f_15_2,plain,
! [U_37,U_36,U_35,U_34] :
( subset(cartesian_product2(U_37,U_35),cartesian_product2(U_36,U_34))
| ~ subset(U_35,U_34)
| ~ subset(U_37,U_36) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( subset(cartesian_product2(U_37,U_35),cartesian_product2(U_36,U_34))
| ~ subset(U_35,U_34)
| ~ subset(U_37,U_36) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B,C] :
( ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[t12_relset_1]) ).
fof(f_16_2,plain,
! [U_40,U_39,U_38] :
( ( subset(relation_rng(U_38),U_39)
& subset(relation_dom(U_38),U_40) )
| ~ relation_of2_as_subset(U_38,U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( subset(relation_dom(U_38),U_40)
| ~ relation_of2_as_subset(U_38,U_40,U_39) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,negated_conjecture,
~ ! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
inference(negate,[status(cth)],[t14_relset_1]) ).
fof(f_17_2,negated_conjecture,
? [A,B,C,D] :
( ~ relation_of2_as_subset(D,C,B)
& subset(relation_rng(D),B)
& relation_of2_as_subset(D,C,A) ),
inference(fof_nnf,[status(thm)],[f_17_1]) ).
fof(f_17_3,negated_conjecture,
? [U_44,U_43,U_42,U_41] :
( ~ relation_of2_as_subset(U_41,U_42,U_43)
& subset(relation_rng(U_41),U_43)
& relation_of2_as_subset(U_41,U_42,U_44) ),
inference(variable_rename,[status(thm)],[f_17_2]) ).
fof(f_17_4,negated_conjecture,
? [U_43,U_42,U_41] :
( ~ relation_of2_as_subset(U_41,U_42,U_43)
& subset(relation_rng(U_41),U_43)
& relation_of2_as_subset(U_41,U_42,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_44,sK4)],[f_17_3]) ).
fof(f_17_5,negated_conjecture,
? [U_42,U_41] :
( ~ relation_of2_as_subset(U_41,U_42,sK5)
& subset(relation_rng(U_41),sK5)
& relation_of2_as_subset(U_41,U_42,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_43,sK5)],[f_17_4]) ).
fof(f_17_6,negated_conjecture,
? [U_41] :
( ~ relation_of2_as_subset(U_41,sK6,sK5)
& subset(relation_rng(U_41),sK5)
& relation_of2_as_subset(U_41,sK6,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_17_5]) ).
fof(f_17_7,negated_conjecture,
( ~ relation_of2_as_subset(sK7,sK6,sK5)
& subset(relation_rng(sK7),sK5)
& relation_of2_as_subset(sK7,sK6,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7)],[f_17_6]) ).
fof(f_17_8,negated_conjecture,
( ~ relation_of2_as_subset(sK7,sK6,sK5)
& subset(relation_rng(sK7),sK5)
& relation_of2_as_subset(sK7,sK6,sK4) ),
inference(definitional_conversion,[status(esa)],[f_17_7]) ).
cnf(f_17_9,negated_conjecture,
relation_of2_as_subset(sK7,sK6,sK4),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_10,negated_conjecture,
subset(relation_rng(sK7),sK5),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_11,negated_conjecture,
~ relation_of2_as_subset(sK7,sK6,sK5),
inference(clausify,[status(thm)],[f_17_8]) ).
fof(f_18_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_18_2,plain,
! [U_47,U_46,U_45] :
( subset(U_47,U_45)
| ~ subset(U_46,U_45)
| ~ subset(U_47,U_46) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( subset(U_47,U_45)
| ~ subset(U_46,U_45)
| ~ subset(U_47,U_46) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t21_relat_1]) ).
fof(f_19_2,plain,
! [U_48] :
( subset(U_48,cartesian_product2(relation_dom(U_48),relation_rng(U_48)))
| ~ relation(U_48) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( subset(U_48,cartesian_product2(relation_dom(U_48),relation_rng(U_48)))
| ~ relation(U_48) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(t1,plain,
~ relation_of2_as_subset(sK7,sK6,sK5),
inference(start,[status(thm),parent(0:0)],[f_17_11]) ).
cnf(t2,plain,
( ~ relation_of2(sK7,sK6,sK5)
| relation_of2_as_subset(sK7,sK6,sK5) ),
inference(extension,[status(thm),parent(t1:1)],[f_13_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ subset(sK7,cartesian_product2(sK6,sK5))
| relation_of2(sK7,sK6,sK5) ),
inference(extension,[status(thm),parent(t2:2)],[f_2_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ subset(cartesian_product2(relation_dom(sK7),relation_rng(sK7)),cartesian_product2(sK6,sK5))
| ~ subset(sK7,cartesian_product2(relation_dom(sK7),relation_rng(sK7)))
| subset(sK7,cartesian_product2(sK6,sK5)) ),
inference(extension,[status(thm),parent(t4:2)],[f_18_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ relation(sK7)
| subset(sK7,cartesian_product2(relation_dom(sK7),relation_rng(sK7))) ),
inference(extension,[status(thm),parent(t6:2)],[f_19_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ element(sK7,powerset(cartesian_product2(sK6,sK4)))
| relation(sK7) ),
inference(extension,[status(thm),parent(t8:2)],[f_1_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ relation_of2_as_subset(sK7,sK6,sK4)
| element(sK7,powerset(cartesian_product2(sK6,sK4))) ),
inference(extension,[status(thm),parent(t10:2)],[f_9_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
relation_of2_as_subset(sK7,sK6,sK4),
inference(extension,[status(thm),parent(t12:2)],[f_17_9]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ subset(cartesian_product2(relation_dom(sK7),sK5),cartesian_product2(sK6,sK5))
| ~ subset(cartesian_product2(relation_dom(sK7),relation_rng(sK7)),cartesian_product2(relation_dom(sK7),sK5))
| subset(cartesian_product2(relation_dom(sK7),relation_rng(sK7)),cartesian_product2(sK6,sK5)) ),
inference(extension,[status(thm),parent(t6:3)],[f_18_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:3]) ).
cnf(t18,plain,
( ~ subset(cartesian_product2(relation_dom(sK7),sK5),cartesian_product2(relation_dom(sK7),sK5))
| ~ subset(cartesian_product2(relation_dom(sK7),relation_rng(sK7)),cartesian_product2(relation_dom(sK7),sK5))
| subset(cartesian_product2(relation_dom(sK7),relation_rng(sK7)),cartesian_product2(relation_dom(sK7),sK5)) ),
inference(extension,[status(thm),parent(t16:2)],[f_18_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ subset(relation_rng(sK7),sK5)
| ~ subset(relation_dom(sK7),relation_dom(sK7))
| subset(cartesian_product2(relation_dom(sK7),relation_rng(sK7)),cartesian_product2(relation_dom(sK7),sK5)) ),
inference(extension,[status(thm),parent(t18:2)],[f_15_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
subset(relation_dom(sK7),relation_dom(sK7)),
inference(extension,[status(thm),parent(t20:2)],[f_14_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
subset(relation_rng(sK7),sK5),
inference(extension,[status(thm),parent(t20:3)],[f_17_10]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( ~ subset(sK5,sK5)
| ~ subset(relation_dom(sK7),relation_dom(sK7))
| subset(cartesian_product2(relation_dom(sK7),sK5),cartesian_product2(relation_dom(sK7),sK5)) ),
inference(extension,[status(thm),parent(t18:3)],[f_15_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t18:3]) ).
cnf(t28,plain,
subset(relation_dom(sK7),relation_dom(sK7)),
inference(extension,[status(thm),parent(t26:2)],[f_14_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
subset(sK5,sK5),
inference(extension,[status(thm),parent(t26:3)],[f_14_4]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
( ~ subset(sK5,sK5)
| ~ subset(relation_dom(sK7),sK6)
| subset(cartesian_product2(relation_dom(sK7),sK5),cartesian_product2(sK6,sK5)) ),
inference(extension,[status(thm),parent(t16:3)],[f_15_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t16:3]) ).
cnf(t34,plain,
( ~ relation_of2_as_subset(sK7,sK6,sK4)
| subset(relation_dom(sK7),sK6) ),
inference(extension,[status(thm),parent(t32:2)],[f_16_3]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
relation_of2_as_subset(sK7,sK6,sK4),
inference(extension,[status(thm),parent(t34:2)],[f_17_9]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
subset(sK5,sK5),
inference(extension,[status(thm),parent(t32:3)],[f_14_4]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t32:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % 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 : n005.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 23:42:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------