%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU030+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 : n012.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 08:57:57 AM UTC 2026
% Result : Theorem 0.76s 1.07s
% Output : Proof 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 86 ( 51 unt; 0 def)
% Number of atoms : 241 ( 77 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 243 ( 88 ~; 80 |; 60 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 25 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(l72_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ! [D] :
( ( function(D)
& relation(D) )
=> ( ( relation_composition(C,D) = identity_relation(A)
& relation_composition(B,C) = identity_relation(relation_dom(D))
& relation_rng(B) = A )
=> D = B ) ) ) ),
file('theBenchmark.p',l72_funct_1) ).
fof(t55_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t61_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A))
& relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A)) ) ) ),
file('theBenchmark.p',t61_funct_1) ).
fof(t63_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( relation_composition(A,B) = identity_relation(relation_dom(A))
& relation_rng(A) = relation_dom(B)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
file('theBenchmark.p',t63_funct_1) ).
fof(f_5_1,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_5_2,plain,
! [U_5] :
( ( function(function_inverse(U_5))
& relation(function_inverse(U_5)) )
| ~ function(U_5)
| ~ relation(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(function_inverse(U_5))
| ~ function(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( function(function_inverse(U_5))
| ~ function(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_21_1,plain,
! [A,B] :
( ! [C] :
( ! [D] :
( D = B
| relation_composition(C,D) != identity_relation(A)
| relation_composition(B,C) != identity_relation(relation_dom(D))
| relation_rng(B) != A
| ~ function(D)
| ~ relation(D) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[l72_funct_1]) ).
fof(f_21_2,plain,
! [U_28,U_27] :
( ! [U_26] :
( ! [U_25] :
( U_25 = U_27
| relation_composition(U_26,U_25) != identity_relation(U_28)
| relation_composition(U_27,U_26) != identity_relation(relation_dom(U_25))
| relation_rng(U_27) != U_28
| ~ function(U_25)
| ~ relation(U_25) )
| ~ function(U_26)
| ~ relation(U_26) )
| ~ function(U_27)
| ~ relation(U_27) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( U_25 = U_27
| relation_composition(U_26,U_25) != identity_relation(U_28)
| relation_composition(U_27,U_26) != identity_relation(relation_dom(U_25))
| relation_rng(U_27) != U_28
| ~ function(U_25)
| ~ relation(U_25)
| ~ function(U_26)
| ~ relation(U_26)
| ~ function(U_27)
| ~ relation(U_27) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_37_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t55_funct_1]) ).
fof(f_37_2,plain,
! [U_56] :
( ( relation_dom(U_56) = relation_rng(function_inverse(U_56))
& relation_rng(U_56) = relation_dom(function_inverse(U_56)) )
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_4,plain,
( relation_dom(U_56) = relation_rng(function_inverse(U_56))
| ~ one_to_one(U_56)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_39_1,plain,
! [A] :
( ( relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A))
& relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t61_funct_1]) ).
fof(f_39_2,plain,
! [U_60] :
( ( relation_composition(function_inverse(U_60),U_60) = identity_relation(relation_rng(U_60))
& relation_composition(U_60,function_inverse(U_60)) = identity_relation(relation_dom(U_60)) )
| ~ one_to_one(U_60)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_4,plain,
( relation_composition(function_inverse(U_60),U_60) = identity_relation(relation_rng(U_60))
| ~ one_to_one(U_60)
| ~ function(U_60)
| ~ relation(U_60) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( relation_composition(A,B) = identity_relation(relation_dom(A))
& relation_rng(A) = relation_dom(B)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
inference(negate,[status(cth)],[t63_funct_1]) ).
fof(f_40_2,negated_conjecture,
? [A] :
( ? [B] :
( B != function_inverse(A)
& relation_composition(A,B) = identity_relation(relation_dom(A))
& relation_rng(A) = relation_dom(B)
& one_to_one(A)
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_40_1]) ).
fof(f_40_3,negated_conjecture,
? [U_62] :
( ? [U_61] :
( U_61 != function_inverse(U_62)
& relation_composition(U_62,U_61) = identity_relation(relation_dom(U_62))
& relation_rng(U_62) = relation_dom(U_61)
& one_to_one(U_62)
& function(U_61)
& relation(U_61) )
& function(U_62)
& relation(U_62) ),
inference(variable_rename,[status(thm)],[f_40_2]) ).
fof(f_40_4,negated_conjecture,
( ? [U_61] :
( U_61 != function_inverse(sK12)
& relation_composition(sK12,U_61) = identity_relation(relation_dom(sK12))
& relation_rng(sK12) = relation_dom(U_61)
& one_to_one(sK12)
& function(U_61)
& relation(U_61) )
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_62,sK12)],[f_40_3]) ).
fof(f_40_5,negated_conjecture,
( sK13 != function_inverse(sK12)
& relation_composition(sK12,sK13) = identity_relation(relation_dom(sK12))
& relation_rng(sK12) = relation_dom(sK13)
& one_to_one(sK12)
& function(sK13)
& relation(sK13)
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_61,sK13)],[f_40_4]) ).
fof(f_40_6,negated_conjecture,
( sK13 != function_inverse(sK12)
& relation_composition(sK12,sK13) = identity_relation(relation_dom(sK12))
& relation_rng(sK12) = relation_dom(sK13)
& one_to_one(sK12)
& function(sK13)
& relation(sK13)
& function(sK12)
& relation(sK12) ),
inference(definitional_conversion,[status(esa)],[f_40_5]) ).
cnf(f_40_7,negated_conjecture,
relation(sK12),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_8,negated_conjecture,
function(sK12),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_9,negated_conjecture,
relation(sK13),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_10,negated_conjecture,
function(sK13),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_11,negated_conjecture,
one_to_one(sK12),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_12,negated_conjecture,
relation_rng(sK12) = relation_dom(sK13),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_13,negated_conjecture,
relation_composition(sK12,sK13) = identity_relation(relation_dom(sK12)),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_14,negated_conjecture,
sK13 != function_inverse(sK12),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_6,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
sK13 != function_inverse(sK12),
inference(start,[status(thm),parent(0:0)],[f_40_14]) ).
cnf(t2,plain,
( ~ function(function_inverse(sK12))
| ~ relation(sK12)
| ~ function(sK12)
| ~ relation(sK13)
| ~ function(sK13)
| relation_rng(function_inverse(sK12)) != relation_dom(sK12)
| relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_dom(sK13))
| relation_composition(sK12,sK13) != identity_relation(relation_dom(sK12))
| ~ relation(function_inverse(sK12))
| sK13 = function_inverse(sK12) ),
inference(extension,[status(thm),parent(t1:1)],[f_21_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ function(sK12)
| ~ relation(sK12)
| relation(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t2:2)],[f_5_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(sK12),
inference(extension,[status(thm),parent(t4:2)],[f_40_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
function(sK12),
inference(extension,[status(thm),parent(t4:3)],[f_40_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
relation_composition(sK12,sK13) = identity_relation(relation_dom(sK12)),
inference(extension,[status(thm),parent(t2:3)],[f_40_13]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( identity_relation(relation_rng(sK12)) != identity_relation(relation_dom(sK13))
| relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_dom(sK13)) ),
inference(extension,[status(thm),parent(t2:4)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
( ~ function(sK12)
| ~ one_to_one(sK12)
| ~ relation(sK12)
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12)) ),
inference(extension,[status(thm),parent(t12:2)],[f_39_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
relation(sK12),
inference(extension,[status(thm),parent(t14:2)],[f_40_7]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
one_to_one(sK12),
inference(extension,[status(thm),parent(t14:3)],[f_40_11]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
function(sK12),
inference(extension,[status(thm),parent(t14:4)],[f_40_8]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
( relation_rng(sK12) != relation_dom(sK13)
| identity_relation(relation_rng(sK12)) = identity_relation(relation_dom(sK13)) ),
inference(extension,[status(thm),parent(t12:3)],[equality_6]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t12:3]) ).
cnf(t24,plain,
relation_rng(sK12) = relation_dom(sK13),
inference(extension,[status(thm),parent(t22:2)],[f_40_12]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( relation_dom(sK12) != relation_rng(function_inverse(sK12))
| relation_rng(function_inverse(sK12)) = relation_dom(sK12) ),
inference(extension,[status(thm),parent(t2:5)],[equality_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t2:5]) ).
cnf(t28,plain,
( ~ function(sK12)
| ~ one_to_one(sK12)
| ~ relation(sK12)
| relation_dom(sK12) = relation_rng(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t26:2)],[f_37_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
relation(sK12),
inference(extension,[status(thm),parent(t28:2)],[f_40_7]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
one_to_one(sK12),
inference(extension,[status(thm),parent(t28:3)],[f_40_11]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
function(sK12),
inference(extension,[status(thm),parent(t28:4)],[f_40_8]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:4]) ).
cnf(t36,plain,
function(sK13),
inference(extension,[status(thm),parent(t2:6)],[f_40_10]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t2:6]) ).
cnf(t38,plain,
relation(sK13),
inference(extension,[status(thm),parent(t2:7)],[f_40_9]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t2:7]) ).
cnf(t40,plain,
function(sK12),
inference(extension,[status(thm),parent(t2:8)],[f_40_8]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t2:8]) ).
cnf(l20,lemma,
function(sK12),
inference(lemma,[status(cth),parent(t2:8),below(t1:1)],[t2:8]) ).
cnf(t42,plain,
relation(sK12),
inference(extension,[status(thm),parent(t2:9)],[f_40_7]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t2:9]) ).
cnf(l21,lemma,
relation(sK12),
inference(lemma,[status(cth),parent(t2:9),below(t1:1)],[t2:9]) ).
cnf(t44,plain,
( ~ function(sK12)
| ~ relation(sK12)
| function(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t2:10)],[f_5_4]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t2:10]) ).
cnf(t46,plain,
relation(sK12),
inference(lemma_extension,[status(thm),parent(t44:2)],[l21:1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
function(sK12),
inference(lemma_extension,[status(thm),parent(t44:3)],[l20:1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU030+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 19 23:13:22 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.76/1.07 % SZS status Theorem for theBenchmark
% 0.76/1.07 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------