%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET657+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 02:14:54 PM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 15 unt; 0 def)
% Number of atoms : 317 ( 13 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 387 ( 155 ~; 156 |; 22 &)
% ( 6 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 172 ( 6 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(p22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(p21,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
fof(p37,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p37) ).
fof(p35,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> range(X1,X2,X3) = range_of(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p35) ).
fof(prove_relset_1_19,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> subset(field_of(X3),union(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_19) ).
fof(p33,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> domain(X1,X2,X3) = domain_of(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(p16,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
fof(p36,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p36) ).
fof(p34,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(domain(X1,X2,X3),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(p9,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( ( subset(X3,X4)
& subset(X1,X2) )
=> subset(union(X1,X3),union(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> field_of(X1) = union(domain_of(X1),range_of(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( ilf_type(X1,set_type)
& relation_like(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(c_0_16,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
fof(c_0_17,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(power_set(X1),set_type)
& ~ empty(power_set(X1)) ) ),
inference(fof_simplification,[status(thm)],[p22]) ).
fof(c_0_18,plain,
! [X44,X45,X46] :
( ( ~ ilf_type(X44,set_type)
| ~ ilf_type(X45,set_type)
| member(X44,power_set(X45))
| ~ member(esk5_2(X44,X45),X45) )
& ( ~ ilf_type(X44,set_type)
| ~ ilf_type(X45,set_type)
| member(X44,power_set(X45))
| member(esk5_2(X44,X45),X44) )
& ( ~ ilf_type(X44,set_type)
| ~ ilf_type(X45,set_type)
| member(X44,power_set(X45))
| ilf_type(esk5_2(X44,X45),set_type) )
& ( ~ ilf_type(X44,set_type)
| ~ ilf_type(X45,set_type)
| member(X46,X45)
| ~ member(X46,X44)
| ~ ilf_type(X46,set_type)
| ~ member(X44,power_set(X45)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p21])])])])])]) ).
fof(c_0_19,plain,
! [X93] : ilf_type(X93,set_type),
inference(variable_rename,[status(thm)],[p37]) ).
fof(c_0_20,plain,
! [X49,X50] :
( ( ~ ilf_type(X49,set_type)
| ~ ilf_type(X50,set_type)
| empty(X50)
| ilf_type(X49,member_type(X50))
| ~ member(X49,X50) )
& ( ~ ilf_type(X49,set_type)
| ~ ilf_type(X50,set_type)
| empty(X50)
| member(X49,X50)
| ~ ilf_type(X49,member_type(X50)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_21,plain,
! [X48] :
( ( ~ ilf_type(X48,set_type)
| ilf_type(power_set(X48),set_type) )
& ( ~ ilf_type(X48,set_type)
| ~ empty(power_set(X48)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_22,plain,
! [X87,X88,X89] :
( range(X87,X88,X89) = range_of(X89)
| ~ ilf_type(X89,relation_type(X87,X88))
| ~ ilf_type(X88,set_type)
| ~ ilf_type(X87,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p35])])])]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> subset(field_of(X3),union(X1,X2)) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_19]) ).
fof(c_0_24,plain,
! [X81,X82,X83] :
( domain(X81,X82,X83) = domain_of(X83)
| ~ ilf_type(X83,relation_type(X81,X82))
| ~ ilf_type(X82,set_type)
| ~ ilf_type(X81,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p33])])])]) ).
cnf(c_0_25,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X1,power_set(X2))
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,member_type(X2))
| empty(X2)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X36,X37] :
( ( ~ ilf_type(X36,set_type)
| ~ ilf_type(X37,set_type)
| ilf_type(X37,subset_type(X36))
| ~ ilf_type(X37,member_type(power_set(X36))) )
& ( ~ ilf_type(X36,set_type)
| ~ ilf_type(X37,set_type)
| ilf_type(X37,member_type(power_set(X36)))
| ~ ilf_type(X37,subset_type(X36)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p16])])])])]) ).
fof(c_0_30,plain,
! [X90,X91,X92] :
( ilf_type(range(X90,X91,X92),subset_type(X91))
| ~ ilf_type(X92,relation_type(X90,X91))
| ~ ilf_type(X91,set_type)
| ~ ilf_type(X90,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p36])])])]) ).
cnf(c_0_31,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| range(X1,X2,X3) = range_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_32,negated_conjecture,
( ~ subset(field_of(esk14_0),union(esk12_0,esk13_0))
& ilf_type(esk14_0,relation_type(esk12_0,esk13_0))
& ilf_type(esk13_0,set_type)
& ilf_type(esk12_0,set_type) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_33,plain,
! [X84,X85,X86] :
( ilf_type(domain(X84,X85,X86),subset_type(X84))
| ~ ilf_type(X86,relation_type(X84,X85))
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p34])])])]) ).
cnf(c_0_34,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| domain(X1,X2,X3) = domain_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,plain,
( ~ member(X1,X3)
| ~ member(X3,power_set(X2))
| member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_36,plain,
( ~ ilf_type(X2,member_type(X1))
| member(X2,X1)
| empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_26]),c_0_26])]) ).
cnf(c_0_37,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_26])]) ).
cnf(c_0_38,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X2))
| ilf_type(X1,member_type(power_set(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(range(X1,X2,X3),subset_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| range(X1,X2,X3) = range_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_26]),c_0_26])]) ).
cnf(c_0_41,negated_conjecture,
ilf_type(esk14_0,relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(domain(X1,X2,X3),subset_type(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| domain(X1,X2,X3) = domain_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_26]),c_0_26])]) ).
cnf(c_0_44,plain,
( ~ ilf_type(X3,member_type(power_set(X2)))
| ~ member(X1,X3)
| member(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_45,plain,
( ~ ilf_type(X1,subset_type(X2))
| ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_26]),c_0_26])]) ).
cnf(c_0_46,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(range(X1,X2,X3),subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_26]),c_0_26])]) ).
cnf(c_0_47,negated_conjecture,
range(esk12_0,esk13_0,esk14_0) = range_of(esk14_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_48,plain,
! [X24,X25,X26] :
( ( ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| subset(X24,X25)
| ~ member(esk2_2(X24,X25),X25) )
& ( ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| subset(X24,X25)
| member(esk2_2(X24,X25),X24) )
& ( ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| subset(X24,X25)
| ilf_type(esk2_2(X24,X25),set_type) )
& ( ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| member(X26,X25)
| ~ member(X26,X24)
| ~ ilf_type(X26,set_type)
| ~ subset(X24,X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p9])])])])])]) ).
cnf(c_0_49,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X3),subset_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_26]),c_0_26])]) ).
cnf(c_0_50,negated_conjecture,
domain(esk12_0,esk13_0,esk14_0) = domain_of(esk14_0),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
fof(c_0_51,plain,
! [X5,X6,X7,X8] :
( subset(union(X5,X7),union(X6,X8))
| ~ subset(X7,X8)
| ~ subset(X5,X6)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_52,plain,
( ~ ilf_type(X3,subset_type(X2))
| ~ member(X1,X3)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
ilf_type(range_of(esk14_0),subset_type(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_41])]) ).
cnf(c_0_54,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,negated_conjecture,
ilf_type(domain_of(esk14_0),subset_type(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_41])]) ).
fof(c_0_56,plain,
! [X64,X65,X66] :
( relation_like(X66)
| ~ ilf_type(X66,subset_type(cross_product(X64,X65)))
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])])]) ).
fof(c_0_57,plain,
! [X17,X18,X19,X20] :
( ( ~ ilf_type(X17,set_type)
| ~ ilf_type(X18,set_type)
| ilf_type(X20,subset_type(cross_product(X17,X18)))
| ~ ilf_type(X20,relation_type(X17,X18)) )
& ( ~ ilf_type(X17,set_type)
| ~ ilf_type(X18,set_type)
| ilf_type(X19,relation_type(X17,X18))
| ~ ilf_type(X19,subset_type(cross_product(X17,X18))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])]) ).
cnf(c_0_58,plain,
( ~ subset(X3,X4)
| ~ subset(X1,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| subset(union(X1,X3),union(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_59,plain,
! [X9] :
( field_of(X9) = union(domain_of(X9),range_of(X9))
| ~ ilf_type(X9,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
cnf(c_0_60,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(X1,range_of(esk14_0))
| member(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_26]),c_0_26])]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(X1,domain_of(esk14_0))
| member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
fof(c_0_64,plain,
! [X34] :
( ( ~ ilf_type(X34,set_type)
| ilf_type(X34,binary_relation_type)
| ~ ilf_type(X34,set_type)
| ~ relation_like(X34) )
& ( ~ ilf_type(X34,set_type)
| ~ ilf_type(X34,binary_relation_type)
| ilf_type(X34,set_type) )
& ( ~ ilf_type(X34,set_type)
| ~ ilf_type(X34,binary_relation_type)
| relation_like(X34) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p14])])])]) ).
cnf(c_0_65,plain,
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,plain,
( ~ subset(X1,X3)
| ~ subset(X2,X4)
| subset(union(X1,X2),union(X3,X4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_26]),c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_68,plain,
( ~ ilf_type(X1,binary_relation_type)
| field_of(X1) = union(domain_of(X1),range_of(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
( ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_26]),c_0_26])]) ).
cnf(c_0_70,negated_conjecture,
( subset(range_of(esk14_0),X1)
| member(esk2_2(range_of(esk14_0),X1),esk13_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( subset(domain_of(esk14_0),X1)
| member(esk2_2(domain_of(esk14_0),X1),esk12_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
cnf(c_0_72,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_73,plain,
( ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_26]),c_0_26])]) ).
cnf(c_0_74,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_26]),c_0_26])]) ).
cnf(c_0_75,negated_conjecture,
~ subset(field_of(esk14_0),union(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_76,plain,
( ~ ilf_type(X1,binary_relation_type)
| ~ subset(domain_of(X1),X2)
| ~ subset(range_of(X1),X3)
| subset(field_of(X1),union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
subset(range_of(esk14_0),esk13_0),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,negated_conjecture,
subset(domain_of(esk14_0),esk12_0),
inference(spm,[status(thm)],[c_0_69,c_0_71]) ).
cnf(c_0_79,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_72]) ).
cnf(c_0_80,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| relation_like(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
~ ilf_type(esk14_0,binary_relation_type),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78])]) ).
cnf(c_0_82,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_26])]) ).
cnf(c_0_83,negated_conjecture,
relation_like(esk14_0),
inference(spm,[status(thm)],[c_0_80,c_0_41]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET657+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 21 05:30:53 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.32 Running first-order theorem proving
% 0.05/0.32 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Version: 3.5.1
% 0.07/0.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/0.36 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.36 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.36 % Starting sh5l with 300s (1) cores
% 0.07/0.36 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1647172 completed with status 0
% 0.07/0.36 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.07/0.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.36 % No SInE strategy applied
% 0.07/0.36 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.07/0.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.07/0.36 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with 209s (1) cores
% 0.07/0.36 % Starting new_bool_3 with 189s (1) cores
% 0.07/0.36 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.07/0.36 % G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with pid 1647180 completed with status 0
% 0.07/0.36 % Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S0Y
% 0.07/0.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.07/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.07/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.36 % No SInE strategy applied
% 0.07/0.36 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.07/0.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.07/0.36 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S0Y with 209s (1) cores
% 0.07/0.36 % Preprocessing time : 0.001 s
% 0.07/0.36
% 0.07/0.36 % Proof found!
% 0.07/0.36 % SZS status Theorem
% 0.07/0.36 % SZS output start CNFRefutation
% See solution above
% 0.07/0.36 % Parsed axioms : 38
% 0.07/0.36 % Removed by relevancy pruning/SinE : 0
% 0.07/0.36 % Initial clauses : 66
% 0.07/0.36 % Removed in clause preprocessing : 5
% 0.07/0.36 % Initial clauses in saturation : 61
% 0.07/0.36 % Processed clauses : 536
% 0.07/0.36 % ...of these trivial : 24
% 0.07/0.36 % ...subsumed : 217
% 0.07/0.36 % ...remaining for further processing : 295
% 0.07/0.36 % Other redundant clauses eliminated : 1
% 0.07/0.36 % Clauses deleted for lack of memory : 0
% 0.07/0.36 % Backward-subsumed : 0
% 0.07/0.36 % Backward-rewritten : 2
% 0.07/0.36 % Generated clauses : 1390
% 0.07/0.36 % ...of the previous two non-redundant : 1323
% 0.07/0.36 % ...aggressively subsumed : 0
% 0.07/0.36 % Contextual simplify-reflections : 3
% 0.07/0.36 % Paramodulations : 1379
% 0.07/0.36 % Factorizations : 10
% 0.07/0.36 % NegExts : 0
% 0.07/0.36 % Equation resolutions : 1
% 0.07/0.36 % Disequality decompositions : 0
% 0.07/0.36 % Total rewrite steps : 185
% 0.07/0.36 % ...of those cached : 132
% 0.07/0.36 % Propositional unsat checks : 0
% 0.07/0.36 % Propositional check models : 0
% 0.07/0.36 % Propositional check unsatisfiable : 0
% 0.07/0.36 % Propositional clauses : 0
% 0.07/0.36 % Propositional clauses after purity: 0
% 0.07/0.36 % Propositional unsat core size : 0
% 0.07/0.36 % Propositional preprocessing time : 0.000
% 0.07/0.36 % Propositional encoding time : 0.000
% 0.07/0.36 % Propositional solver time : 0.000
% 0.07/0.36 % Success case prop preproc time : 0.000
% 0.07/0.36 % Success case prop encoding time : 0.000
% 0.07/0.36 % Success case prop solver time : 0.000
% 0.07/0.36 % Current number of processed clauses : 293
% 0.07/0.36 % Positive orientable unit clauses : 46
% 0.07/0.36 % Positive unorientable unit clauses: 1
% 0.07/0.36 % Negative unit clauses : 4
% 0.07/0.36 % Non-unit-clauses : 242
% 0.07/0.36 % Current number of unprocessed clauses: 848
% 0.07/0.36 % ...number of literals in the above : 2625
% 0.07/0.36 % Current number of archived formulas : 0
% 0.07/0.36 % Current number of archived clauses : 2
% 0.07/0.36 % Clause-clause subsumption calls (NU) : 12968
% 0.07/0.36 % Rec. Clause-clause subsumption calls : 11343
% 0.07/0.36 % Non-unit clause-clause subsumptions : 212
% 0.07/0.36 % Unit Clause-clause subsumption calls : 513
% 0.07/0.36 % Rewrite failures with RHS unbound : 0
% 0.07/0.36 % BW rewrite match attempts : 40
% 0.07/0.36 % BW rewrite match successes : 6
% 0.07/0.36 % Condensation attempts : 0
% 0.07/0.36 % Condensation successes : 0
% 0.07/0.36 % Termbank termtop insertions : 24418
% 0.07/0.36 % Search garbage collected termcells : 1389
% 0.07/0.36
% 0.07/0.36 % -------------------------------------------------
% 0.07/0.36 % User time : 0.027 s
% 0.07/0.36 % System time : 0.002 s
% 0.07/0.36 % Total time : 0.029 s
% 0.07/0.36 % Maximum resident set size: 3680 pages
% 0.07/0.36
% 0.07/0.36 % -------------------------------------------------
% 0.07/0.36 % User time : 0.095 s
% 0.07/0.36 % System time : 0.013 s
% 0.07/0.36 % Total time : 0.108 s
% 0.07/0.36 % Maximum resident set size: 4864 pages
% 0.07/0.36 % E exiting
%------------------------------------------------------------------------------