%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU125+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n004.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 08:58:06 AM UTC 2026
% Result : Theorem 1.66s 2.02s
% Output : Proof 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 22 unt; 0 def)
% Number of atoms : 174 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 192 ( 69 ~; 65 |; 52 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn 67 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t8_xboole_1,conjecture,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(f_2_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_3_2,plain,
! [U_8,U_7,U_6] :
( ( U_6 = set_union2(U_8,U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& ( in(U_5,U_7)
| in(U_5,U_8) ) )
| ( ~ in(U_5,U_7)
& ~ in(U_5,U_8)
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| ( ~ in(U_4,U_7)
& ~ in(U_4,U_8) ) )
& ( in(U_4,U_7)
| in(U_4,U_8)
| ~ in(U_4,U_6) ) )
| U_6 != set_union2(U_8,U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( in(U_12,U_16)
| in(U_12,U_18) ) )
| ? [U_11] :
( ~ in(U_11,U_16)
& ~ in(U_11,U_18)
& in(U_11,U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( in(U_12,U_16)
| in(U_12,U_18) ) )
| ( ~ in(sK1(U_18,U_16,U_14),U_16)
& ~ in(sK1(U_18,U_16,U_14),U_18)
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_18,U_16,U_14))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ( ~ in(sK2(U_18,U_16,U_14),U_14)
& ( in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18) ) )
| ( ~ in(sK1(U_18,U_16,U_14),U_16)
& ~ in(sK1(U_18,U_16,U_14),U_18)
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_12,sK2(U_18,U_16,U_14))],[f_3_4]) ).
cnf(f_3_6,plain,
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13)
| U_13 != set_union2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_4_2,plain,
! [U_22,U_21] :
( ( subset(U_22,U_21)
| ? [U_20] :
( ~ in(U_20,U_21)
& in(U_20,U_22) ) )
& ( ! [U_19] :
( in(U_19,U_21)
| ~ in(U_19,U_22) )
| ~ subset(U_22,U_21) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_26,U_24] :
( subset(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_24)
& in(U_20,U_26) ) )
& ! [U_25,U_23] :
( ! [U_19] :
( in(U_19,U_23)
| ~ in(U_19,U_25) )
| ~ subset(U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_26,U_24] :
( subset(U_26,U_24)
| ( ~ in(sK3(U_26,U_24),U_24)
& in(sK3(U_26,U_24),U_26) ) )
& ! [U_25,U_23] :
( ! [U_19] :
( in(U_19,U_23)
| ~ in(U_19,U_25) )
| ~ subset(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3(U_26,U_24))],[f_4_3]) ).
cnf(f_4_5,plain,
( in(U_19,U_23)
| ~ in(U_19,U_25)
| ~ subset(U_25,U_23) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( in(sK3(U_26,U_24),U_26)
| subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( ~ in(sK3(U_26,U_24),U_24)
| subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_18_1,negated_conjecture,
~ ! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
inference(negate,[status(cth)],[t8_xboole_1]) ).
fof(f_18_2,negated_conjecture,
? [A,B,C] :
( ~ subset(set_union2(A,C),B)
& subset(C,B)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_45,U_44,U_43] :
( ~ subset(set_union2(U_45,U_43),U_44)
& subset(U_43,U_44)
& subset(U_45,U_44) ),
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
? [U_44,U_43] :
( ~ subset(set_union2(sK6,U_43),U_44)
& subset(U_43,U_44)
& subset(sK6,U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_45,sK6)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
? [U_43] :
( ~ subset(set_union2(sK6,U_43),sK7)
& subset(U_43,sK7)
& subset(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_44,sK7)],[f_18_4]) ).
fof(f_18_6,negated_conjecture,
( ~ subset(set_union2(sK6,sK8),sK7)
& subset(sK8,sK7)
& subset(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8)],[f_18_5]) ).
fof(f_18_7,negated_conjecture,
( ~ subset(set_union2(sK6,sK8),sK7)
& subset(sK8,sK7)
& subset(sK6,sK7) ),
inference(definitional_conversion,[status(esa)],[f_18_6]) ).
cnf(f_18_8,negated_conjecture,
subset(sK6,sK7),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_9,negated_conjecture,
subset(sK8,sK7),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_10,negated_conjecture,
~ subset(set_union2(sK6,sK8),sK7),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(t1,plain,
~ subset(set_union2(sK6,sK8),sK7),
inference(start,[status(thm),parent(0:0)],[f_18_10]) ).
cnf(t2,plain,
( in(sK3(set_union2(sK6,sK8),sK7),set_union2(sK6,sK8))
| subset(set_union2(sK6,sK8),sK7) ),
inference(extension,[status(thm),parent(t1:1)],[f_4_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( in(sK3(set_union2(sK6,sK8),sK7),sK6)
| in(sK3(set_union2(sK6,sK8),sK7),sK8)
| set_union2(sK6,sK8) != set_union2(sK8,sK6)
| ~ in(sK3(set_union2(sK6,sK8),sK7),set_union2(sK6,sK8)) ),
inference(extension,[status(thm),parent(t2:2)],[f_3_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
set_union2(sK6,sK8) = set_union2(sK8,sK6),
inference(extension,[status(thm),parent(t4:2)],[f_2_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( in(sK3(set_union2(sK6,sK8),sK7),sK7)
| ~ subset(sK8,sK7)
| ~ in(sK3(set_union2(sK6,sK8),sK7),sK8) ),
inference(extension,[status(thm),parent(t4:3)],[f_4_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
subset(sK8,sK7),
inference(extension,[status(thm),parent(t8:2)],[f_18_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( subset(set_union2(sK6,sK8),sK7)
| ~ in(sK3(set_union2(sK6,sK8),sK7),sK7) ),
inference(extension,[status(thm),parent(t8:3)],[f_4_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
$false,
inference(reduction,[status(thm),parent(t12:2)],[t12:2,t1:1]) ).
cnf(t15,plain,
( in(sK3(set_union2(sK6,sK8),sK7),sK7)
| ~ subset(sK6,sK7)
| ~ in(sK3(set_union2(sK6,sK8),sK7),sK6) ),
inference(extension,[status(thm),parent(t4:4)],[f_4_5]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t4:4]) ).
cnf(t17,plain,
subset(sK6,sK7),
inference(extension,[status(thm),parent(t15:2)],[f_18_8]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
( subset(set_union2(sK6,sK8),sK7)
| ~ in(sK3(set_union2(sK6,sK8),sK7),sK7) ),
inference(extension,[status(thm),parent(t15:3)],[f_4_7]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t15:3]) ).
cnf(t21,plain,
$false,
inference(reduction,[status(thm),parent(t19:2)],[t19:2,t1:1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU125+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.07/0.34 % Computer : n004.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 23:20:34 UTC 2026
% 0.07/0.35 % CPUTime :
% 1.66/2.02 % SZS status Theorem for theBenchmark
% 1.66/2.02 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------