%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU080+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n013.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 08:58:01 AM UTC 2026
% Result : Theorem 0.80s 1.06s
% Output : Proof 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 28 unt; 0 def)
% Number of atoms : 141 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 46 ~; 37 |; 45 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 25 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(t158_funct_1,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( subset(A,relation_rng(C))
& subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) )
=> subset(A,B) ) ),
file('theBenchmark.p',t158_funct_1) ).
fof(t161_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( subset(B,relation_rng(C))
& subset(A,relation_rng(C))
& relation_inverse_image(C,A) = relation_inverse_image(C,B) )
=> A = B ) ),
file('theBenchmark.p',t161_funct_1) ).
fof(f_5_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_5_2,plain,
! [U_6,U_5] :
( ( U_6 = U_5
| ~ subset(U_5,U_6)
| ~ subset(U_6,U_5) )
& ( ( subset(U_5,U_6)
& subset(U_6,U_5) )
| U_6 != U_5 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_10,U_8] :
( U_10 = U_8
| ~ subset(U_8,U_10)
| ~ subset(U_10,U_8) )
& ! [U_9,U_7] :
( ( subset(U_7,U_9)
& subset(U_9,U_7) )
| U_9 != U_7 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( subset(U_9,U_7)
| U_9 != U_7 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( subset(U_7,U_9)
| U_9 != U_7 ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( U_10 = U_8
| ~ subset(U_8,U_10)
| ~ subset(U_10,U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_24_1,plain,
! [A,B,C] :
( subset(A,B)
| ~ subset(A,relation_rng(C))
| ~ subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t158_funct_1]) ).
fof(f_24_2,plain,
! [U_32,U_31,U_30] :
( subset(U_32,U_31)
| ~ subset(U_32,relation_rng(U_30))
| ~ subset(relation_inverse_image(U_30,U_32),relation_inverse_image(U_30,U_31))
| ~ function(U_30)
| ~ relation(U_30) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( subset(U_32,U_31)
| ~ subset(U_32,relation_rng(U_30))
| ~ subset(relation_inverse_image(U_30,U_32),relation_inverse_image(U_30,U_31))
| ~ function(U_30)
| ~ relation(U_30) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( subset(B,relation_rng(C))
& subset(A,relation_rng(C))
& relation_inverse_image(C,A) = relation_inverse_image(C,B) )
=> A = B ) ),
inference(negate,[status(cth)],[t161_funct_1]) ).
fof(f_25_2,negated_conjecture,
? [A,B,C] :
( A != B
& subset(B,relation_rng(C))
& subset(A,relation_rng(C))
& relation_inverse_image(C,A) = relation_inverse_image(C,B)
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_25_1]) ).
fof(f_25_3,negated_conjecture,
? [U_35,U_34,U_33] :
( U_35 != U_34
& subset(U_34,relation_rng(U_33))
& subset(U_35,relation_rng(U_33))
& relation_inverse_image(U_33,U_35) = relation_inverse_image(U_33,U_34)
& function(U_33)
& relation(U_33) ),
inference(variable_rename,[status(thm)],[f_25_2]) ).
fof(f_25_4,negated_conjecture,
? [U_34,U_33] :
( sK12 != U_34
& subset(U_34,relation_rng(U_33))
& subset(sK12,relation_rng(U_33))
& relation_inverse_image(U_33,sK12) = relation_inverse_image(U_33,U_34)
& function(U_33)
& relation(U_33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_35,sK12)],[f_25_3]) ).
fof(f_25_5,negated_conjecture,
? [U_33] :
( sK12 != sK13
& subset(sK13,relation_rng(U_33))
& subset(sK12,relation_rng(U_33))
& relation_inverse_image(U_33,sK12) = relation_inverse_image(U_33,sK13)
& function(U_33)
& relation(U_33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_34,sK13)],[f_25_4]) ).
fof(f_25_6,negated_conjecture,
( sK12 != sK13
& subset(sK13,relation_rng(sK14))
& subset(sK12,relation_rng(sK14))
& relation_inverse_image(sK14,sK12) = relation_inverse_image(sK14,sK13)
& function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_33,sK14)],[f_25_5]) ).
fof(f_25_7,negated_conjecture,
( sK12 != sK13
& subset(sK13,relation_rng(sK14))
& subset(sK12,relation_rng(sK14))
& relation_inverse_image(sK14,sK12) = relation_inverse_image(sK14,sK13)
& function(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_25_6]) ).
cnf(f_25_8,negated_conjecture,
relation(sK14),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_9,negated_conjecture,
function(sK14),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_10,negated_conjecture,
relation_inverse_image(sK14,sK12) = relation_inverse_image(sK14,sK13),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_11,negated_conjecture,
subset(sK12,relation_rng(sK14)),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_12,negated_conjecture,
subset(sK13,relation_rng(sK14)),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_13,negated_conjecture,
sK12 != sK13,
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(t1,plain,
sK12 != sK13,
inference(start,[status(thm),parent(0:0)],[f_25_13]) ).
cnf(t2,plain,
( ~ subset(sK13,sK12)
| ~ subset(sK12,sK13)
| sK12 = sK13 ),
inference(extension,[status(thm),parent(t1:1)],[f_5_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ function(sK14)
| ~ subset(relation_inverse_image(sK14,sK12),relation_inverse_image(sK14,sK13))
| ~ subset(sK12,relation_rng(sK14))
| ~ relation(sK14)
| subset(sK12,sK13) ),
inference(extension,[status(thm),parent(t2:2)],[f_24_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(sK14),
inference(extension,[status(thm),parent(t4:2)],[f_25_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
subset(sK12,relation_rng(sK14)),
inference(extension,[status(thm),parent(t4:3)],[f_25_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( relation_inverse_image(sK14,sK12) != relation_inverse_image(sK14,sK13)
| subset(relation_inverse_image(sK14,sK12),relation_inverse_image(sK14,sK13)) ),
inference(extension,[status(thm),parent(t4:4)],[f_5_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
relation_inverse_image(sK14,sK12) = relation_inverse_image(sK14,sK13),
inference(extension,[status(thm),parent(t10:2)],[f_25_10]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
function(sK14),
inference(extension,[status(thm),parent(t4:5)],[f_25_9]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:5]) ).
cnf(t16,plain,
( ~ function(sK14)
| ~ subset(relation_inverse_image(sK14,sK13),relation_inverse_image(sK14,sK12))
| ~ subset(sK13,relation_rng(sK14))
| ~ relation(sK14)
| subset(sK13,sK12) ),
inference(extension,[status(thm),parent(t2:3)],[f_24_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
relation(sK14),
inference(extension,[status(thm),parent(t16:2)],[f_25_8]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
subset(sK13,relation_rng(sK14)),
inference(extension,[status(thm),parent(t16:3)],[f_25_12]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( relation_inverse_image(sK14,sK12) != relation_inverse_image(sK14,sK13)
| subset(relation_inverse_image(sK14,sK13),relation_inverse_image(sK14,sK12)) ),
inference(extension,[status(thm),parent(t16:4)],[f_5_5]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:4]) ).
cnf(t24,plain,
relation_inverse_image(sK14,sK12) = relation_inverse_image(sK14,sK13),
inference(extension,[status(thm),parent(t22:2)],[f_25_10]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
function(sK14),
inference(extension,[status(thm),parent(t16:5)],[f_25_9]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t16:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU080+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 23:18:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.80/1.06 % SZS status Theorem for theBenchmark
% 0.80/1.06 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------