%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET677+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 : 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 08:57:16 AM UTC 2026
% Result : Theorem 1.80s 2.04s
% Output : Proof 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 37 unt; 0 def)
% Number of atoms : 160 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 162 ( 64 ~; 56 |; 25 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 1 sgn 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( C = range(B,C,D)
& subset(C,domain(B,C,D)) ) ) ) ) ),
file('theBenchmark.p',p2) ).
fof(p5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('theBenchmark.p',p5) ).
fof(p34,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p34) ).
fof(prove_relset_1_44,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( subset(identity_relation_of(B),C)
=> ( B = range(B,B,C)
& B = domain(B,B,C) ) ) ) ),
file('theBenchmark.p',prove_relset_1_44) ).
fof(f_1_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(C,range(C,B,D))
& C = domain(C,B,D) )
| ~ subset(identity_relation_of(C),D)
| ~ ilf_type(D,relation_type(C,B)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_1_2,plain,
! [U_2] :
( ! [U_1] :
( ! [U_0] :
( ( subset(U_1,range(U_1,U_2,U_0))
& U_1 = domain(U_1,U_2,U_0) )
| ~ subset(identity_relation_of(U_1),U_0)
| ~ ilf_type(U_0,relation_type(U_1,U_2)) )
| ~ ilf_type(U_1,set_type) )
| ~ ilf_type(U_2,set_type) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( U_1 = domain(U_1,U_2,U_0)
| ~ subset(identity_relation_of(U_1),U_0)
| ~ ilf_type(U_0,relation_type(U_1,U_2))
| ~ ilf_type(U_1,set_type)
| ~ ilf_type(U_2,set_type) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( C = range(B,C,D)
& subset(C,domain(B,C,D)) )
| ~ subset(identity_relation_of(C),D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p2]) ).
fof(f_2_2,plain,
! [U_5] :
( ! [U_4] :
( ! [U_3] :
( ( U_4 = range(U_5,U_4,U_3)
& subset(U_4,domain(U_5,U_4,U_3)) )
| ~ subset(identity_relation_of(U_4),U_3)
| ~ ilf_type(U_3,relation_type(U_5,U_4)) )
| ~ ilf_type(U_4,set_type) )
| ~ ilf_type(U_5,set_type) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_4,plain,
( U_4 = range(U_5,U_4,U_3)
| ~ subset(identity_relation_of(U_4),U_3)
| ~ ilf_type(U_3,relation_type(U_5,U_4))
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_5_1,plain,
! [B] :
( ! [C] :
( ( ( ilf_type(C,identity_relation_of_type(B))
| ~ ilf_type(C,relation_type(B,B)) )
& ( ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,identity_relation_of_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p5]) ).
fof(f_5_2,plain,
! [U_11] :
( ! [U_10] :
( ( ( ilf_type(U_10,identity_relation_of_type(U_11))
| ~ ilf_type(U_10,relation_type(U_11,U_11)) )
& ( ilf_type(U_10,relation_type(U_11,U_11))
| ~ ilf_type(U_10,identity_relation_of_type(U_11)) ) )
| ~ ilf_type(U_10,set_type) )
| ~ ilf_type(U_11,set_type) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ilf_type(U_10,relation_type(U_11,U_11))
| ~ ilf_type(U_10,identity_relation_of_type(U_11))
| ~ ilf_type(U_10,set_type)
| ~ ilf_type(U_11,set_type) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_34_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p34]) ).
fof(f_34_2,plain,
! [U_82] : ilf_type(U_82,set_type),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
ilf_type(U_82,set_type),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( subset(identity_relation_of(B),C)
=> ( B = range(B,B,C)
& B = domain(B,B,C) ) ) ) ),
inference(negate,[status(cth)],[prove_relset_1_44]) ).
fof(f_35_2,negated_conjecture,
? [B] :
( ? [C] :
( ( B != range(B,B,C)
| B != domain(B,B,C) )
& subset(identity_relation_of(B),C)
& ilf_type(C,identity_relation_of_type(B)) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
? [U_84] :
( ? [U_83] :
( ( U_84 != range(U_84,U_84,U_83)
| U_84 != domain(U_84,U_84,U_83) )
& subset(identity_relation_of(U_84),U_83)
& ilf_type(U_83,identity_relation_of_type(U_84)) )
& ilf_type(U_84,set_type) ),
inference(variable_rename,[status(thm)],[f_35_2]) ).
fof(f_35_4,negated_conjecture,
( ? [U_83] :
( ( sK14 != range(sK14,sK14,U_83)
| sK14 != domain(sK14,sK14,U_83) )
& subset(identity_relation_of(sK14),U_83)
& ilf_type(U_83,identity_relation_of_type(sK14)) )
& ilf_type(sK14,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_84,sK14)],[f_35_3]) ).
fof(f_35_5,negated_conjecture,
( ( sK14 != range(sK14,sK14,sK15)
| sK14 != domain(sK14,sK14,sK15) )
& subset(identity_relation_of(sK14),sK15)
& ilf_type(sK15,identity_relation_of_type(sK14))
& ilf_type(sK14,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_83,sK15)],[f_35_4]) ).
fof(f_35_6,negated_conjecture,
( ( sK14 != range(sK14,sK14,sK15)
| sK14 != domain(sK14,sK14,sK15) )
& subset(identity_relation_of(sK14),sK15)
& ilf_type(sK15,identity_relation_of_type(sK14))
& ilf_type(sK14,set_type) ),
inference(definitional_conversion,[status(esa)],[f_35_5]) ).
cnf(f_35_7,negated_conjecture,
ilf_type(sK14,set_type),
inference(clausify,[status(thm)],[f_35_6]) ).
cnf(f_35_8,negated_conjecture,
ilf_type(sK15,identity_relation_of_type(sK14)),
inference(clausify,[status(thm)],[f_35_6]) ).
cnf(f_35_9,negated_conjecture,
subset(identity_relation_of(sK14),sK15),
inference(clausify,[status(thm)],[f_35_6]) ).
cnf(f_35_10,negated_conjecture,
( sK14 != range(sK14,sK14,sK15)
| sK14 != domain(sK14,sK14,sK15) ),
inference(clausify,[status(thm)],[f_35_6]) ).
cnf(t1,plain,
( sK14 != range(sK14,sK14,sK15)
| sK14 != domain(sK14,sK14,sK15) ),
inference(start,[status(thm),parent(0:0)],[f_35_10]) ).
cnf(t2,plain,
( ~ ilf_type(sK14,set_type)
| ~ ilf_type(sK15,relation_type(sK14,sK14))
| ~ subset(identity_relation_of(sK14),sK15)
| ~ ilf_type(sK14,set_type)
| sK14 = domain(sK14,sK14,sK15) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
ilf_type(sK14,set_type),
inference(extension,[status(thm),parent(t2:2)],[f_35_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(l2,lemma,
ilf_type(sK14,set_type),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t6,plain,
subset(identity_relation_of(sK14),sK15),
inference(extension,[status(thm),parent(t2:3)],[f_35_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ ilf_type(sK15,set_type)
| ~ ilf_type(sK15,identity_relation_of_type(sK14))
| ~ ilf_type(sK14,set_type)
| ilf_type(sK15,relation_type(sK14,sK14)) ),
inference(extension,[status(thm),parent(t2:4)],[f_5_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
ilf_type(sK14,set_type),
inference(lemma_extension,[status(thm),parent(t8:2)],[l2:1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
ilf_type(sK15,identity_relation_of_type(sK14)),
inference(extension,[status(thm),parent(t8:3)],[f_35_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
ilf_type(sK15,set_type),
inference(extension,[status(thm),parent(t8:4)],[f_34_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:4]) ).
cnf(t16,plain,
ilf_type(sK14,set_type),
inference(lemma_extension,[status(thm),parent(t2:5)],[l2:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:5]) ).
cnf(t18,plain,
( ~ ilf_type(sK14,set_type)
| ~ ilf_type(sK15,relation_type(sK14,sK14))
| ~ subset(identity_relation_of(sK14),sK15)
| ~ ilf_type(sK14,set_type)
| sK14 = range(sK14,sK14,sK15) ),
inference(extension,[status(thm),parent(t1:2)],[f_2_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t1:2]) ).
cnf(t20,plain,
ilf_type(sK14,set_type),
inference(extension,[status(thm),parent(t18:2)],[f_35_7]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(l8,lemma,
ilf_type(sK14,set_type),
inference(lemma,[status(cth),parent(t18:2),below(t1:2)],[t18:2]) ).
cnf(t22,plain,
subset(identity_relation_of(sK14),sK15),
inference(extension,[status(thm),parent(t18:3)],[f_35_9]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( ~ ilf_type(sK15,set_type)
| ~ ilf_type(sK15,identity_relation_of_type(sK14))
| ~ ilf_type(sK14,set_type)
| ilf_type(sK15,relation_type(sK14,sK14)) ),
inference(extension,[status(thm),parent(t18:4)],[f_5_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:4]) ).
cnf(t26,plain,
ilf_type(sK14,set_type),
inference(lemma_extension,[status(thm),parent(t24:2)],[l8:1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
ilf_type(sK15,identity_relation_of_type(sK14)),
inference(extension,[status(thm),parent(t24:3)],[f_35_8]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
ilf_type(sK15,set_type),
inference(extension,[status(thm),parent(t24:4)],[f_34_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t24:4]) ).
cnf(t32,plain,
ilf_type(sK14,set_type),
inference(lemma_extension,[status(thm),parent(t18:5)],[l8:1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t18:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET677+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 22:46:46 UTC 2026
% 0.07/0.35 % CPUTime :
% 1.80/2.04 % SZS status Theorem for theBenchmark
% 1.80/2.04 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------