%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU026+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 : n018.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 3.27s 3.54s
% Output : Proof 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 105 ( 62 unt; 0 def)
% Number of atoms : 222 ( 64 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 204 ( 87 ~; 80 |; 24 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 49 ( 3 sgn 27 !; 2 ?)
% 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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t46_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t47_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_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(t59_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_rng(relation_composition(function_inverse(A),A)) = relation_rng(A)
& relation_dom(relation_composition(function_inverse(A),A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t59_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]) ).
fof(f_29_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_29_2,plain,
! [U_34,U_33] : subset(U_34,U_34),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_34] : subset(U_34,U_34),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
subset(U_34,U_34),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_33_1,plain,
! [A] :
( ! [B] :
( relation_dom(relation_composition(A,B)) = relation_dom(A)
| ~ subset(relation_rng(A),relation_dom(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t46_relat_1]) ).
fof(f_33_2,plain,
! [U_46] :
( ! [U_45] :
( relation_dom(relation_composition(U_46,U_45)) = relation_dom(U_46)
| ~ subset(relation_rng(U_46),relation_dom(U_45))
| ~ relation(U_45) )
| ~ relation(U_46) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( relation_dom(relation_composition(U_46,U_45)) = relation_dom(U_46)
| ~ subset(relation_rng(U_46),relation_dom(U_45))
| ~ relation(U_45)
| ~ relation(U_46) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(B,A)) = relation_rng(A)
| ~ subset(relation_dom(A),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t47_relat_1]) ).
fof(f_34_2,plain,
! [U_48] :
( ! [U_47] :
( relation_rng(relation_composition(U_47,U_48)) = relation_rng(U_48)
| ~ subset(relation_dom(U_48),relation_rng(U_47))
| ~ relation(U_47) )
| ~ relation(U_48) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( relation_rng(relation_composition(U_47,U_48)) = relation_rng(U_48)
| ~ subset(relation_dom(U_48),relation_rng(U_47))
| ~ relation(U_47)
| ~ relation(U_48) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_36_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_36_2,plain,
! [U_52] :
( ( relation_dom(U_52) = relation_rng(function_inverse(U_52))
& relation_rng(U_52) = relation_dom(function_inverse(U_52)) )
| ~ one_to_one(U_52)
| ~ function(U_52)
| ~ relation(U_52) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( relation_rng(U_52) = relation_dom(function_inverse(U_52))
| ~ one_to_one(U_52)
| ~ function(U_52)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( relation_dom(U_52) = relation_rng(function_inverse(U_52))
| ~ one_to_one(U_52)
| ~ function(U_52)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_rng(relation_composition(function_inverse(A),A)) = relation_rng(A)
& relation_dom(relation_composition(function_inverse(A),A)) = relation_rng(A) ) ) ),
inference(negate,[status(cth)],[t59_funct_1]) ).
fof(f_37_2,negated_conjecture,
? [A] :
( ( relation_rng(relation_composition(function_inverse(A),A)) != relation_rng(A)
| relation_dom(relation_composition(function_inverse(A),A)) != relation_rng(A) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_37_1]) ).
fof(f_37_3,negated_conjecture,
? [U_53] :
( ( relation_rng(relation_composition(function_inverse(U_53),U_53)) != relation_rng(U_53)
| relation_dom(relation_composition(function_inverse(U_53),U_53)) != relation_rng(U_53) )
& one_to_one(U_53)
& function(U_53)
& relation(U_53) ),
inference(variable_rename,[status(thm)],[f_37_2]) ).
fof(f_37_4,negated_conjecture,
( ( relation_rng(relation_composition(function_inverse(sK12),sK12)) != relation_rng(sK12)
| relation_dom(relation_composition(function_inverse(sK12),sK12)) != relation_rng(sK12) )
& one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_53,sK12)],[f_37_3]) ).
fof(f_37_5,negated_conjecture,
( ( relation_rng(relation_composition(function_inverse(sK12),sK12)) != relation_rng(sK12)
| relation_dom(relation_composition(function_inverse(sK12),sK12)) != relation_rng(sK12) )
& one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(definitional_conversion,[status(esa)],[f_37_4]) ).
cnf(f_37_6,negated_conjecture,
relation(sK12),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_7,negated_conjecture,
function(sK12),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_8,negated_conjecture,
one_to_one(sK12),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_9,negated_conjecture,
( relation_rng(relation_composition(function_inverse(sK12),sK12)) != relation_rng(sK12)
| relation_dom(relation_composition(function_inverse(sK12),sK12)) != relation_rng(sK12) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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_7,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( relation_rng(relation_composition(function_inverse(sK12),sK12)) != relation_rng(sK12)
| relation_dom(relation_composition(function_inverse(sK12),sK12)) != relation_rng(sK12) ),
inference(start,[status(thm),parent(0:0)],[f_37_9]) ).
cnf(t2,plain,
( relation_dom(function_inverse(sK12)) != relation_rng(sK12)
| relation_dom(relation_composition(function_inverse(sK12),sK12)) != relation_dom(function_inverse(sK12))
| relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ relation(sK12)
| ~ subset(relation_rng(function_inverse(sK12)),relation_dom(sK12))
| ~ relation(function_inverse(sK12))
| relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_dom(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t2:2)],[f_33_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ function(sK12)
| ~ relation(sK12)
| relation(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t4:2)],[f_5_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
relation(sK12),
inference(extension,[status(thm),parent(t6:2)],[f_37_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
function(sK12),
inference(extension,[status(thm),parent(t6:3)],[f_37_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( relation_dom(sK12) != relation_dom(sK12)
| ~ subset(relation_dom(sK12),relation_dom(sK12))
| relation_dom(sK12) != relation_rng(function_inverse(sK12))
| subset(relation_rng(function_inverse(sK12)),relation_dom(sK12)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_19]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
( ~ function(sK12)
| ~ one_to_one(sK12)
| ~ relation(sK12)
| relation_dom(sK12) = relation_rng(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t12:2)],[f_36_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_37_6]) ).
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_37_8]) ).
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_37_7]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
subset(relation_dom(sK12),relation_dom(sK12)),
inference(extension,[status(thm),parent(t12:3)],[f_29_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t12:3]) ).
cnf(t24,plain,
( sK12 != sK12
| relation_dom(sK12) = relation_dom(sK12) ),
inference(extension,[status(thm),parent(t12:4)],[equality_7]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t12:4]) ).
cnf(t26,plain,
sK12 = sK12,
inference(extension,[status(thm),parent(t24:2)],[equality_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
relation(sK12),
inference(extension,[status(thm),parent(t4:4)],[f_37_6]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t4:4]) ).
cnf(t30,plain,
( relation_rng(sK12) != relation_dom(function_inverse(sK12))
| relation_dom(function_inverse(sK12)) = relation_rng(sK12) ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t2:3]) ).
cnf(t32,plain,
( ~ function(sK12)
| ~ one_to_one(sK12)
| ~ relation(sK12)
| relation_rng(sK12) = relation_dom(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t30:2)],[f_36_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
relation(sK12),
inference(extension,[status(thm),parent(t32:2)],[f_37_6]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
one_to_one(sK12),
inference(extension,[status(thm),parent(t32:3)],[f_37_8]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
function(sK12),
inference(extension,[status(thm),parent(t32:4)],[f_37_7]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t32:4]) ).
cnf(t40,plain,
( ~ relation(function_inverse(sK12))
| ~ subset(relation_dom(sK12),relation_rng(function_inverse(sK12)))
| ~ relation(sK12)
| relation_rng(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12) ),
inference(extension,[status(thm),parent(t1:2)],[f_34_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t1:2]) ).
cnf(t42,plain,
relation(sK12),
inference(extension,[status(thm),parent(t40:2)],[f_37_6]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(l21,lemma,
relation(sK12),
inference(lemma,[status(cth),parent(t40:2),below(t1:2)],[t40:2]) ).
cnf(t44,plain,
( relation_dom(sK12) != relation_rng(function_inverse(sK12))
| ~ subset(relation_dom(sK12),relation_dom(sK12))
| relation_dom(sK12) != relation_dom(sK12)
| subset(relation_dom(sK12),relation_rng(function_inverse(sK12))) ),
inference(extension,[status(thm),parent(t40:3)],[equality_19]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
( sK12 != sK12
| relation_dom(sK12) = relation_dom(sK12) ),
inference(extension,[status(thm),parent(t44:2)],[equality_7]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
( sK12 != sK12
| sK12 = sK12 ),
inference(extension,[status(thm),parent(t46:2)],[equality_2]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
sK12 = sK12,
inference(extension,[status(thm),parent(t48:2)],[equality_1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
subset(relation_dom(sK12),relation_dom(sK12)),
inference(extension,[status(thm),parent(t44:3)],[f_29_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t44:3]) ).
cnf(t54,plain,
( ~ function(sK12)
| ~ one_to_one(sK12)
| ~ relation(sK12)
| relation_dom(sK12) = relation_rng(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t44:4)],[f_36_4]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t44:4]) ).
cnf(t56,plain,
relation(sK12),
inference(lemma_extension,[status(thm),parent(t54:2)],[l21:1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
one_to_one(sK12),
inference(extension,[status(thm),parent(t54:3)],[f_37_8]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
function(sK12),
inference(extension,[status(thm),parent(t54:4)],[f_37_7]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t54:4]) ).
cnf(t62,plain,
( ~ function(sK12)
| ~ relation(sK12)
| relation(function_inverse(sK12)) ),
inference(extension,[status(thm),parent(t40:4)],[f_5_3]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t40:4]) ).
cnf(t64,plain,
relation(sK12),
inference(lemma_extension,[status(thm),parent(t62:2)],[l21:1]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
function(sK12),
inference(extension,[status(thm),parent(t62:3)],[f_37_7]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t62:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU026+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
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:15:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 3.27/3.54 % SZS status Theorem for theBenchmark
% 3.27/3.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------