%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU353+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 05:11:34 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 121 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 133 ( 57 ~; 43 |; 20 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-4 aty)
% Number of variables : 61 ( 0 sgn 39 !; 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/sandbox/benchmark/theBenchmark.p',t91_tmap_1) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(t35_funct_1,axiom,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(redefinition_k6_partfun1,axiom,
! [X1] : identity_as_relation_of(X1) = identity_relation(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(d11_grcat_1,axiom,
! [X1] :
( one_sorted_str(X1)
=> identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_grcat_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(c_0_9,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_10,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_11,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_12,negated_conjecture,
( ~ empty_carrier(esk16_0)
& one_sorted_str(esk16_0)
& element(esk17_0,the_carrier(esk16_0))
& apply_as_element(the_carrier(esk16_0),the_carrier(esk16_0),identity_on_carrier(esk16_0),esk17_0) != esk17_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X147] :
( empty_carrier(X147)
| ~ one_sorted_str(X147)
| ~ empty(the_carrier(X147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
fof(c_0_14,plain,
! [X173,X174,X175,X176] :
( empty(X173)
| ~ function(X175)
| ~ quasi_total(X175,X173,X174)
| ~ relation_of2(X175,X173,X174)
| ~ element(X176,X173)
| apply_as_element(X173,X174,X175,X176) = apply(X175,X176) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_15,negated_conjecture,
~ empty_carrier(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
one_sorted_str(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
apply_as_element(the_carrier(esk16_0),the_carrier(esk16_0),identity_on_carrier(esk16_0),esk17_0) != esk17_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,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_14]) ).
cnf(c_0_20,negated_conjecture,
element(esk17_0,the_carrier(esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
~ empty(the_carrier(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
fof(c_0_22,plain,
! [X130] :
( ( function(identity_on_carrier(X130))
| ~ one_sorted_str(X130) )
& ( quasi_total(identity_on_carrier(X130),the_carrier(X130),the_carrier(X130))
| ~ one_sorted_str(X130) )
& ( relation_of2_as_subset(identity_on_carrier(X130),the_carrier(X130),the_carrier(X130))
| ~ one_sorted_str(X130) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_grcat_1])])]) ).
fof(c_0_23,plain,
! [X177,X178,X179] :
( ( ~ relation_of2_as_subset(X179,X177,X178)
| relation_of2(X179,X177,X178) )
& ( ~ relation_of2(X179,X177,X178)
| relation_of2_as_subset(X179,X177,X178) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_24,plain,
! [X185,X186] :
( ~ in(X186,X185)
| apply(identity_relation(X185),X186) = X186 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_funct_1])]) ).
fof(c_0_25,plain,
! [X172] : identity_as_relation_of(X172) = identity_relation(X172),
inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).
cnf(c_0_26,negated_conjecture,
( apply(identity_on_carrier(esk16_0),esk17_0) != esk17_0
| ~ quasi_total(identity_on_carrier(esk16_0),the_carrier(esk16_0),the_carrier(esk16_0))
| ~ function(identity_on_carrier(esk16_0))
| ~ relation_of2(identity_on_carrier(esk16_0),the_carrier(esk16_0),the_carrier(esk16_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_27,plain,
( quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( apply(identity_relation(X2),X1) = X1
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
identity_as_relation_of(X1) = identity_relation(X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X127] :
( ~ one_sorted_str(X127)
| identity_on_carrier(X127) = identity_as_relation_of(the_carrier(X127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_grcat_1])]) ).
cnf(c_0_33,negated_conjecture,
( apply(identity_on_carrier(esk16_0),esk17_0) != esk17_0
| ~ function(identity_on_carrier(esk16_0))
| ~ relation_of2(identity_on_carrier(esk16_0),the_carrier(esk16_0),the_carrier(esk16_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17])]) ).
cnf(c_0_34,plain,
( relation_of2(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( apply(identity_as_relation_of(X2),X1) = X1
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( apply(identity_on_carrier(esk16_0),esk17_0) != esk17_0
| ~ function(identity_on_carrier(esk16_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_17])]) ).
cnf(c_0_38,plain,
( apply(identity_on_carrier(X1),X2) = X2
| ~ one_sorted_str(X1)
| ~ in(X2,the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_39,plain,
! [X183,X184] :
( ~ element(X183,X184)
| empty(X184)
| in(X183,X184) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_40,negated_conjecture,
( ~ function(identity_on_carrier(esk16_0))
| ~ in(esk17_0,the_carrier(esk16_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_17])]) ).
cnf(c_0_41,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_42,negated_conjecture,
~ function(identity_on_carrier(esk16_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_20])]),c_0_21]) ).
cnf(c_0_43,plain,
( function(identity_on_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU353+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 03:00:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------