%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU353+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:35 PM UTC 2026
% Result : Theorem 13.44s 8.44s
% Output : CNFRefutation 13.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 144 ( 26 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 140 ( 51 ~; 39 |; 29 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-4 aty)
% Number of variables : 69 ( 1 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t91_tmap_1,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tmap_1) ).
fof(d11_grcat_1,axiom,
! [X1] :
( one_sorted_str(X1)
=> identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).
fof(redefinition_k6_partfun1,axiom,
! [X1] : identity_as_relation_of(X1) = identity_relation(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(dt_k6_partfun1,axiom,
! [X1] :
( v1_partfun1(identity_as_relation_of(X1),X1,X1)
& relation_of2_as_subset(identity_as_relation_of(X1),X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(redefinition_k8_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2)
& element(X4,X1) )
=> apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
fof(dt_k7_grcat_1,axiom,
! [X1] :
( one_sorted_str(X1)
=> ( function(identity_on_carrier(X1))
& quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(t35_funct_1,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t91_tmap_1])]) ).
fof(c_0_13,plain,
! [X1897] :
( ~ one_sorted_str(X1897)
| identity_on_carrier(X1897) = identity_as_relation_of(the_carrier(X1897)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_grcat_1])]) ).
fof(c_0_14,plain,
! [X2847] : identity_as_relation_of(X2847) = identity_relation(X2847),
inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).
fof(c_0_15,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
fof(c_0_16,plain,
! [X2218] :
( ~ one_sorted_str(X2218)
| cast_as_carrier_subset(X2218) = the_carrier(X2218) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
fof(c_0_17,negated_conjecture,
( ~ empty_carrier(esk440_0)
& one_sorted_str(esk440_0)
& element(esk441_0,the_carrier(esk440_0))
& apply_as_element(the_carrier(esk440_0),the_carrier(esk440_0),identity_on_carrier(esk440_0),esk441_0) != esk441_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_18,plain,
( identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
identity_as_relation_of(X1) = identity_relation(X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X2492] :
( v1_partfun1(identity_as_relation_of(X2492),X2492,X2492)
& relation_of2_as_subset(identity_as_relation_of(X2492),X2492,X2492) ),
inference(variable_rename,[status(thm)],[dt_k6_partfun1]) ).
fof(c_0_21,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_22,plain,
! [X2587] :
( empty_carrier(X2587)
| ~ one_sorted_str(X2587)
| ~ empty(cast_as_carrier_subset(X2587)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_23,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
one_sorted_str(esk440_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2)
& element(X4,X1) )
=> apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k8_funct_2]) ).
fof(c_0_26,plain,
! [X2501] :
( ( function(identity_on_carrier(X2501))
| ~ one_sorted_str(X2501) )
& ( quasi_total(identity_on_carrier(X2501),the_carrier(X2501),the_carrier(X2501))
| ~ one_sorted_str(X2501) )
& ( relation_of2_as_subset(identity_on_carrier(X2501),the_carrier(X2501),the_carrier(X2501))
| ~ one_sorted_str(X2501) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_grcat_1])])]) ).
cnf(c_0_27,plain,
( identity_on_carrier(X1) = identity_relation(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_28,plain,
! [X2857,X2858,X2859] :
( ( ~ relation_of2_as_subset(X2859,X2857,X2858)
| relation_of2(X2859,X2857,X2858) )
& ( ~ relation_of2(X2859,X2857,X2858)
| relation_of2_as_subset(X2859,X2857,X2858) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_29,plain,
relation_of2_as_subset(identity_as_relation_of(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_30,plain,
! [X2156,X2157] :
( ( ~ element(X2157,X2156)
| in(X2157,X2156)
| empty(X2156) )
& ( ~ in(X2157,X2156)
| element(X2157,X2156)
| empty(X2156) )
& ( ~ element(X2157,X2156)
| empty(X2157)
| ~ empty(X2156) )
& ( ~ empty(X2157)
| element(X2157,X2156)
| ~ empty(X2156) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_31,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(cast_as_carrier_subset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,negated_conjecture,
cast_as_carrier_subset(esk440_0) = the_carrier(esk440_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,negated_conjecture,
~ empty_carrier(esk440_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_34,plain,
! [X2853,X2854,X2855,X2856] :
( empty(X2853)
| ~ function(X2855)
| ~ quasi_total(X2855,X2853,X2854)
| ~ relation_of2(X2855,X2853,X2854)
| ~ element(X2856,X2853)
| apply_as_element(X2853,X2854,X2855,X2856) = apply(X2855,X2856) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
cnf(c_0_35,plain,
( quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
identity_on_carrier(esk440_0) = identity_relation(the_carrier(esk440_0)),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_37,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
relation_of2_as_subset(identity_relation(X1),X1,X1),
inference(rw,[status(thm)],[c_0_29,c_0_19]) ).
fof(c_0_39,plain,
! [X2582] :
( relation(identity_relation(X2582))
& function(identity_relation(X2582)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_40,lemma,
! [X3675,X3676] :
( ~ in(X3676,X3675)
| apply(identity_relation(X3675),X3676) = X3676 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_funct_1])]) ).
cnf(c_0_41,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,negated_conjecture,
element(esk441_0,the_carrier(esk440_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_43,negated_conjecture,
~ empty(the_carrier(esk440_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24])]),c_0_33]) ).
cnf(c_0_44,plain,
( empty(X1)
| apply_as_element(X1,X3,X2,X4) = apply(X2,X4)
| ~ function(X2)
| ~ quasi_total(X2,X1,X3)
| ~ relation_of2(X2,X1,X3)
| ~ element(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,negated_conjecture,
quasi_total(identity_relation(the_carrier(esk440_0)),the_carrier(esk440_0),the_carrier(esk440_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_36]) ).
cnf(c_0_46,plain,
relation_of2(identity_relation(X1),X1,X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,lemma,
( apply(identity_relation(X2),X1) = X1
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,negated_conjecture,
in(esk441_0,the_carrier(esk440_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_50,negated_conjecture,
apply_as_element(the_carrier(esk440_0),the_carrier(esk440_0),identity_on_carrier(esk440_0),esk441_0) != esk441_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_51,negated_conjecture,
( apply_as_element(the_carrier(esk440_0),the_carrier(esk440_0),identity_relation(the_carrier(esk440_0)),X1) = apply(identity_relation(the_carrier(esk440_0)),X1)
| ~ element(X1,the_carrier(esk440_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]),c_0_43]) ).
cnf(c_0_52,negated_conjecture,
apply(identity_relation(the_carrier(esk440_0)),esk441_0) = esk441_0,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
apply_as_element(the_carrier(esk440_0),the_carrier(esk440_0),identity_relation(the_carrier(esk440_0)),esk441_0) != esk441_0,
inference(rw,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_42]),c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU353+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:59:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 13.44/8.44 % Version : CSE_E---1.7
% 13.44/8.44 % Problem : theBenchmark.p
% 13.44/8.44 % SZS status Theorem for theBenchmark.p
% 13.44/8.44 % SZS output start CNFRefutation
% See solution above
% 13.44/8.48 % Total time : 6.605s
%------------------------------------------------------------------------------