%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM383+1 : 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 : n008.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 08:52:08 AM UTC 2026
% Result : Theorem 0.15s 10.54s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 16 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 49 ~; 40 |; 13 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 64 ( 1 sgn 47 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t7_ordinal1,conjecture,
! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
file('theBenchmark.p',t7_ordinal1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_21_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_21_2,plain,
! [U_22,U_21] :
( in(U_22,U_21)
| empty(U_21)
| ~ element(U_22,U_21) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( in(U_22,U_21)
| empty(U_21)
| ~ element(U_22,U_21) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_22_2,plain,
! [U_24,U_23] :
( ( element(U_24,powerset(U_23))
| ~ subset(U_24,U_23) )
& ( subset(U_24,U_23)
| ~ element(U_24,powerset(U_23)) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_28,U_26] :
( element(U_28,powerset(U_26))
| ~ subset(U_28,U_26) )
& ! [U_27,U_25] :
( subset(U_27,U_25)
| ~ element(U_27,powerset(U_25)) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_5,plain,
( element(U_28,powerset(U_26))
| ~ subset(U_28,U_26) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_23_2,plain,
! [U_31,U_30,U_29] :
( element(U_31,U_29)
| ~ element(U_30,powerset(U_29))
| ~ in(U_31,U_30) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( element(U_31,U_29)
| ~ element(U_30,powerset(U_29))
| ~ in(U_31,U_30) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_24_2,plain,
! [U_34,U_33,U_32] :
( ~ empty(U_32)
| ~ element(U_33,powerset(U_32))
| ~ in(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_34,U_33] :
( ! [U_32] :
( ~ empty(U_32)
| ~ element(U_33,powerset(U_32)) )
| ~ in(U_34,U_33) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( ~ empty(U_32)
| ~ element(U_33,powerset(U_32))
| ~ in(U_34,U_33) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_27_1,negated_conjecture,
~ ! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
inference(negate,[status(cth)],[t7_ordinal1]) ).
fof(f_27_2,negated_conjecture,
? [A,B] :
( subset(B,A)
& in(A,B) ),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
? [U_39,U_38] :
( subset(U_38,U_39)
& in(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_27_2]) ).
fof(f_27_4,negated_conjecture,
? [U_38] :
( subset(U_38,sK12)
& in(sK12,U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_39,sK12)],[f_27_3]) ).
fof(f_27_5,negated_conjecture,
( subset(sK13,sK12)
& in(sK12,sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_38,sK13)],[f_27_4]) ).
fof(f_27_6,negated_conjecture,
( subset(sK13,sK12)
& in(sK12,sK13) ),
inference(definitional_conversion,[status(esa)],[f_27_5]) ).
cnf(f_27_7,negated_conjecture,
in(sK12,sK13),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_8,negated_conjecture,
subset(sK13,sK12),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(t1,plain,
( ~ element(sK13,powerset(sK12))
| ~ empty(sK12)
| ~ in(sK12,sK13) ),
inference(start,[status(thm),parent(0:0)],[f_24_4]) ).
cnf(t2,plain,
in(sK12,sK13),
inference(extension,[status(thm),parent(t1:1)],[f_27_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( in(sK12,sK12)
| ~ element(sK12,sK12)
| empty(sK12) ),
inference(extension,[status(thm),parent(t1:2)],[f_21_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
( ~ element(sK13,powerset(sK12))
| ~ in(sK12,sK13)
| element(sK12,sK12) ),
inference(extension,[status(thm),parent(t4:2)],[f_23_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
in(sK12,sK13),
inference(extension,[status(thm),parent(t6:2)],[f_27_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ subset(sK13,sK12)
| element(sK13,powerset(sK12)) ),
inference(extension,[status(thm),parent(t6:3)],[f_22_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
subset(sK13,sK12),
inference(extension,[status(thm),parent(t10:2)],[f_27_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ in(sK12,sK12)
| ~ in(sK12,sK12) ),
inference(extension,[status(thm),parent(t4:3)],[f_1_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:3]) ).
cnf(t16,plain,
$false,
inference(reduction,[status(thm),parent(t14:2)],[t14:2,t4:3]) ).
cnf(t17,plain,
( ~ subset(sK13,sK12)
| element(sK13,powerset(sK12)) ),
inference(extension,[status(thm),parent(t1:3)],[f_22_5]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t1:3]) ).
cnf(t19,plain,
subset(sK13,sK12),
inference(extension,[status(thm),parent(t17:2)],[f_27_8]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.10/10.39 % Computer : n008.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Sat Sep 19 18:21:55 UTC 2026
% 0.10/10.40 % CPUTime :
% 0.15/10.54 % SZS status Theorem for theBenchmark
% 0.15/10.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------