%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU355+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 : n022.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 0.41s 1.61s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 101)
% Comments :
%------------------------------------------------------------------------------
fof(t6_yellow_0,conjecture,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc1_finset_1,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(d9_lattice3,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X4,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
fof(d8_lattice3,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(dt_l1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(cc1_finset_1,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(existence_l1_struct_0,axiom,
? [X1] : one_sorted_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l1_orders_2,axiom,
? [X1] : rel_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_18,negated_conjecture,
~ ! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
inference(assume_negation,[status(cth)],[t6_yellow_0]) ).
fof(i_0_19,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_20,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_21,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finset_1]) ).
fof(i_0_22,plain,
! [X43,X44,X45,X46] :
( ( ~ relstr_set_smaller(X43,X44,X45)
| ~ element(X46,the_carrier(X43))
| ~ in(X46,X44)
| related(X43,X46,X45)
| ~ element(X45,the_carrier(X43))
| ~ rel_str(X43) )
& ( element(esk2_3(X43,X44,X45),the_carrier(X43))
| relstr_set_smaller(X43,X44,X45)
| ~ element(X45,the_carrier(X43))
| ~ rel_str(X43) )
& ( in(esk2_3(X43,X44,X45),X44)
| relstr_set_smaller(X43,X44,X45)
| ~ element(X45,the_carrier(X43))
| ~ rel_str(X43) )
& ( ~ related(X43,esk2_3(X43,X44,X45),X45)
| relstr_set_smaller(X43,X44,X45)
| ~ element(X45,the_carrier(X43))
| ~ rel_str(X43) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_lattice3])])])])]) ).
fof(i_0_23,plain,
! [X38,X39,X40,X41] :
( ( ~ relstr_element_smaller(X38,X39,X40)
| ~ element(X41,the_carrier(X38))
| ~ in(X41,X39)
| related(X38,X40,X41)
| ~ element(X40,the_carrier(X38))
| ~ rel_str(X38) )
& ( element(esk1_3(X38,X39,X40),the_carrier(X38))
| relstr_element_smaller(X38,X39,X40)
| ~ element(X40,the_carrier(X38))
| ~ rel_str(X38) )
& ( in(esk1_3(X38,X39,X40),X39)
| relstr_element_smaller(X38,X39,X40)
| ~ element(X40,the_carrier(X38))
| ~ rel_str(X38) )
& ( ~ related(X38,X40,esk1_3(X38,X39,X40))
| relstr_element_smaller(X38,X39,X40)
| ~ element(X40,the_carrier(X38))
| ~ rel_str(X38) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_lattice3])])])])]) ).
fof(i_0_24,negated_conjecture,
( rel_str(esk9_0)
& element(esk10_0,the_carrier(esk9_0))
& ( ~ relstr_set_smaller(esk9_0,empty_set,esk10_0)
| ~ relstr_element_smaller(esk9_0,empty_set,esk10_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])])]) ).
fof(i_0_25,plain,
! [X35,X36] :
( ~ in(X35,X36)
| ~ in(X36,X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_19])]) ).
fof(i_0_26,plain,
! [X58,X59] :
( ~ element(X58,X59)
| empty(X59)
| in(X58,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_27,plain,
! [X56,X57] :
( ~ in(X56,X57)
| element(X56,X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_28,plain,
! [X63,X64] :
( ~ in(X63,X64)
| ~ empty(X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_29,plain,
! [X51] : element(esk5_1(X51),X51),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_30,plain,
! [X65,X66] :
( ~ empty(X65)
| X65 = X66
| ~ empty(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_31,plain,
! [X48] :
( ~ rel_str(X48)
| one_sorted_str(X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).
fof(i_0_32,plain,
! [X37] :
( ~ empty(X37)
| finite(X37) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])]) ).
fof(i_0_33,plain,
! [X60] :
( ~ empty(X60)
| X60 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_34,plain,
~ empty(esk8_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_20])]) ).
fof(i_0_35,plain,
( ~ empty(esk6_0)
& finite(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_21])]) ).
fof(i_0_36,plain,
one_sorted_str(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_struct_0])]) ).
fof(i_0_37,plain,
rel_str(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_orders_2])]) ).
fof(i_0_38,plain,
empty(esk7_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_39,plain,
( relstr_set_smaller(X1,X2,X3)
| ~ related(X1,esk2_3(X1,X2,X3),X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
( relstr_element_smaller(X1,X3,X2)
| ~ related(X1,X2,esk1_3(X1,X3,X2))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_41,plain,
( related(X1,X3,X4)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_42,plain,
( related(X1,X4,X3)
| ~ relstr_set_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_43,plain,
( element(esk2_3(X1,X2,X3),the_carrier(X1))
| relstr_set_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_44,plain,
( element(esk1_3(X1,X2,X3),the_carrier(X1))
| relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_45,plain,
( in(esk2_3(X1,X2,X3),X2)
| relstr_set_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_46,plain,
( in(esk1_3(X1,X2,X3),X2)
| relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_47,negated_conjecture,
( ~ relstr_set_smaller(esk9_0,empty_set,esk10_0)
| ~ relstr_element_smaller(esk9_0,empty_set,esk10_0) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_48,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_49,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_50,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_51,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_52,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_53,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_54,negated_conjecture,
element(esk10_0,the_carrier(esk9_0)),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_55,plain,
( one_sorted_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_56,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_57,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_58,plain,
~ empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_59,plain,
~ empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_60,plain,
one_sorted_str(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_61,negated_conjecture,
rel_str(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_62,plain,
rel_str(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_63,plain,
finite(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_64,plain,
empty(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_65,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_66,axiom,
X1 = X1 ).
cnf(i_0_67,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_68,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_69,axiom,
( X1 != X2
| ~ relstr_set_smaller(X1,X3,X4)
| relstr_set_smaller(X2,X3,X4) ) ).
cnf(i_0_70,axiom,
( X1 != X2
| ~ relstr_set_smaller(X3,X1,X4)
| relstr_set_smaller(X3,X2,X4) ) ).
cnf(i_0_71,axiom,
( X1 != X2
| ~ relstr_set_smaller(X3,X4,X1)
| relstr_set_smaller(X3,X4,X2) ) ).
cnf(i_0_72,axiom,
( X1 != X2
| ~ related(X1,X3,X4)
| related(X2,X3,X4) ) ).
cnf(i_0_73,axiom,
( X1 != X2
| ~ related(X3,X1,X4)
| related(X3,X2,X4) ) ).
cnf(i_0_74,axiom,
( X1 != X2
| ~ related(X3,X4,X1)
| related(X3,X4,X2) ) ).
cnf(i_0_75,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_76,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_77,axiom,
( X1 != X2
| ~ rel_str(X1)
| rel_str(X2) ) ).
cnf(i_0_78,axiom,
( X1 != X2
| ~ relstr_element_smaller(X1,X3,X4)
| relstr_element_smaller(X2,X3,X4) ) ).
cnf(i_0_79,axiom,
( X1 != X2
| ~ relstr_element_smaller(X3,X1,X4)
| relstr_element_smaller(X3,X2,X4) ) ).
cnf(i_0_80,axiom,
( X1 != X2
| ~ relstr_element_smaller(X3,X4,X1)
| relstr_element_smaller(X3,X4,X2) ) ).
cnf(i_0_81,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_82,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_83,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_84,axiom,
( X1 != X2
| ~ one_sorted_str(X1)
| one_sorted_str(X2) ) ).
cnf(i_0_85,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_66_001,axiom,
X1 = X1 ).
cnf(i_0_67_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_68_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_69_004,axiom,
( X1 != X2
| ~ relstr_set_smaller(X1,X3,X4)
| relstr_set_smaller(X2,X3,X4) ) ).
cnf(i_0_70_005,axiom,
( X1 != X2
| ~ relstr_set_smaller(X3,X1,X4)
| relstr_set_smaller(X3,X2,X4) ) ).
cnf(i_0_71_006,axiom,
( X1 != X2
| ~ relstr_set_smaller(X3,X4,X1)
| relstr_set_smaller(X3,X4,X2) ) ).
cnf(i_0_72_007,axiom,
( X1 != X2
| ~ related(X1,X3,X4)
| related(X2,X3,X4) ) ).
cnf(i_0_73_008,axiom,
( X1 != X2
| ~ related(X3,X1,X4)
| related(X3,X2,X4) ) ).
cnf(i_0_74_009,axiom,
( X1 != X2
| ~ related(X3,X4,X1)
| related(X3,X4,X2) ) ).
cnf(i_0_75_010,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_76_011,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_77_012,axiom,
( X1 != X2
| ~ rel_str(X1)
| rel_str(X2) ) ).
cnf(i_0_78_013,axiom,
( X1 != X2
| ~ relstr_element_smaller(X1,X3,X4)
| relstr_element_smaller(X2,X3,X4) ) ).
cnf(i_0_79_014,axiom,
( X1 != X2
| ~ relstr_element_smaller(X3,X1,X4)
| relstr_element_smaller(X3,X2,X4) ) ).
cnf(i_0_80_015,axiom,
( X1 != X2
| ~ relstr_element_smaller(X3,X4,X1)
| relstr_element_smaller(X3,X4,X2) ) ).
cnf(i_0_81_016,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_82_017,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_83_018,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_84_019,axiom,
( X1 != X2
| ~ one_sorted_str(X1)
| one_sorted_str(X2) ) ).
cnf(i_0_85_020,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_86,plain,
one_sorted_str(esk9_0),
inference(scs_inference,[],[i_0_61,i_0_55]) ).
cnf(i_0_87,plain,
( ~ rel_str(X1)
| one_sorted_str(X1) ),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_88,plain,
~ in(X1,esk7_0),
inference(scs_inference,[],[i_0_61,i_0_64,i_0_55,i_0_51]) ).
cnf(i_0_89,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_90,plain,
finite(esk7_0),
inference(scs_inference,[],[i_0_61,i_0_64,i_0_55,i_0_51,i_0_56]) ).
cnf(i_0_91,plain,
( ~ empty(X1)
| finite(X1) ),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_92,plain,
in(esk5_1(esk8_0),esk8_0),
inference(scs_inference,[],[i_0_61,i_0_52,i_0_58,i_0_64,i_0_55,i_0_51,i_0_56,i_0_49]) ).
cnf(i_0_93,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_94,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_95,plain,
esk8_0 != esk7_0,
inference(scs_inference,[],[i_0_61,i_0_52,i_0_58,i_0_64,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82]) ).
cnf(i_0_96,plain,
esk7_0 != esk8_0,
inference(scs_inference,[],[i_0_61,i_0_52,i_0_58,i_0_64,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82,i_0_83]) ).
cnf(i_0_97,plain,
~ in(esk8_0,esk5_1(esk8_0)),
inference(scs_inference,[],[i_0_61,i_0_52,i_0_58,i_0_64,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82,i_0_83,i_0_48]) ).
cnf(i_0_98,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_99,plain,
( empty(the_carrier(esk9_0))
| in(esk10_0,the_carrier(esk9_0)) ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_52,i_0_58,i_0_64,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82,i_0_83,i_0_48,i_0_94]) ).
cnf(i_0_100,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_101,plain,
( rel_str(X1)
| esk9_0 != X1 ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_52,i_0_58,i_0_64,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82,i_0_83,i_0_48,i_0_94,i_0_77]) ).
cnf(i_0_102,plain,
( X1 != esk8_0
| ~ in(X1,esk5_1(esk8_0)) ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_52,i_0_58,i_0_64,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82,i_0_83,i_0_48,i_0_94,i_0_77,i_0_81]) ).
cnf(i_0_103,plain,
( one_sorted_str(X1)
| esk4_0 != X1 ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_52,i_0_58,i_0_64,i_0_60,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82,i_0_83,i_0_48,i_0_94,i_0_77,i_0_81,i_0_84]) ).
cnf(i_0_104,plain,
( finite(X1)
| esk6_0 != X1 ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_52,i_0_58,i_0_64,i_0_60,i_0_63,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82,i_0_83,i_0_48,i_0_94,i_0_77,i_0_81,i_0_84,i_0_85]) ).
cnf(i_0_105,plain,
( relstr_set_smaller(esk9_0,X1,esk10_0)
| ~ related(esk9_0,esk2_3(esk9_0,X1,esk10_0),esk10_0) ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_52,i_0_58,i_0_64,i_0_60,i_0_63,i_0_55,i_0_51,i_0_56,i_0_49,i_0_82,i_0_83,i_0_48,i_0_94,i_0_77,i_0_81,i_0_84,i_0_85,i_0_39]) ).
cnf(i_0_106,plain,
( ~ element(X1,the_carrier(X2))
| ~ related(X2,esk2_3(X2,X3,X1),X1)
| ~ rel_str(X2)
| relstr_set_smaller(X2,X3,X1) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_107,plain,
rel_str(esk9_0),
inference(equality_inference,[],[101]) ).
cnf(i_0_108,plain,
~ in(esk8_0,esk5_1(esk8_0)),
inference(equality_inference,[],[102]) ).
cnf(i_0_109,plain,
one_sorted_str(esk4_0),
inference(equality_inference,[],[103]) ).
cnf(i_0_110,plain,
finite(esk6_0),
inference(equality_inference,[],[104]) ).
cnf(i_0_111,plain,
one_sorted_str(esk3_0),
inference(scs_inference,[],[i_0_62,i_0_55]) ).
cnf(i_0_112,plain,
( ~ rel_str(X1)
| one_sorted_str(X1) ),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_113,plain,
finite(empty_set),
inference(scs_inference,[],[i_0_62,i_0_65,i_0_55,i_0_56]) ).
cnf(i_0_114,plain,
( ~ empty(X1)
| finite(X1) ),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_115,plain,
~ in(X1,empty_set),
inference(scs_inference,[],[i_0_62,i_0_65,i_0_55,i_0_56,i_0_51]) ).
cnf(i_0_116,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_117,plain,
in(esk5_1(esk6_0),esk6_0),
inference(scs_inference,[],[i_0_59,i_0_62,i_0_52,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49]) ).
cnf(i_0_118,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_119,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_120,plain,
esk8_0 != empty_set,
inference(scs_inference,[],[i_0_92,i_0_59,i_0_62,i_0_52,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82]) ).
cnf(i_0_121,plain,
esk7_0 != esk6_0,
inference(scs_inference,[],[i_0_92,i_0_59,i_0_62,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83]) ).
cnf(i_0_122,plain,
relstr_set_smaller(esk9_0,esk7_0,esk10_0),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_88,i_0_59,i_0_62,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45]) ).
cnf(i_0_123,plain,
~ in(X1,esk7_0),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_124,plain,
( ~ element(X1,the_carrier(X2))
| in(esk2_3(X2,X3,X1),X3)
| relstr_set_smaller(X2,X3,X1)
| ~ rel_str(X2) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_125,plain,
relstr_element_smaller(esk9_0,esk7_0,esk10_0),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_88,i_0_123,i_0_59,i_0_62,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45,i_0_46]) ).
cnf(i_0_126,plain,
~ in(X1,esk7_0),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_127,plain,
( ~ element(X1,the_carrier(X2))
| in(esk1_3(X2,X3,X1),X3)
| relstr_element_smaller(X2,X3,X1)
| ~ rel_str(X2) ),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_128,plain,
~ in(esk6_0,esk5_1(esk6_0)),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_88,i_0_123,i_0_59,i_0_62,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45,i_0_46,i_0_48]) ).
cnf(i_0_129,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_130,plain,
( rel_str(X1)
| esk3_0 != X1 ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_88,i_0_123,i_0_59,i_0_62,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45,i_0_46,i_0_48,i_0_77]) ).
cnf(i_0_131,plain,
( X1 != esk6_0
| ~ in(X1,esk5_1(esk6_0)) ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_88,i_0_123,i_0_59,i_0_62,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45,i_0_46,i_0_48,i_0_77,i_0_81]) ).
cnf(i_0_132,plain,
( one_sorted_str(X1)
| esk9_0 != X1 ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_86,i_0_88,i_0_123,i_0_59,i_0_62,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45,i_0_46,i_0_48,i_0_77,i_0_81,i_0_84]) ).
cnf(i_0_133,plain,
( finite(X1)
| esk7_0 != X1 ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_86,i_0_88,i_0_123,i_0_59,i_0_62,i_0_90,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45,i_0_46,i_0_48,i_0_77,i_0_81,i_0_84,i_0_85]) ).
cnf(i_0_134,plain,
( relstr_element_smaller(esk9_0,X1,esk10_0)
| ~ related(esk9_0,esk10_0,esk1_3(esk9_0,X1,esk10_0)) ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_86,i_0_88,i_0_123,i_0_59,i_0_62,i_0_90,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45,i_0_46,i_0_48,i_0_77,i_0_81,i_0_84,i_0_85,i_0_40]) ).
cnf(i_0_135,plain,
( ~ element(X1,the_carrier(X2))
| ~ related(X2,X1,esk1_3(X2,X3,X1))
| ~ rel_str(X2)
| relstr_element_smaller(X2,X3,X1) ),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_136,plain,
( relstr_set_smaller(esk9_0,X1,esk10_0)
| element(esk2_3(esk9_0,X1,esk10_0),the_carrier(esk9_0)) ),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_92,i_0_86,i_0_88,i_0_123,i_0_59,i_0_62,i_0_90,i_0_52,i_0_64,i_0_65,i_0_55,i_0_56,i_0_51,i_0_49,i_0_82,i_0_83,i_0_45,i_0_46,i_0_48,i_0_77,i_0_81,i_0_84,i_0_85,i_0_40,i_0_43]) ).
cnf(i_0_137,plain,
( ~ element(X1,the_carrier(X2))
| element(esk2_3(X2,X3,X1),the_carrier(X2))
| relstr_set_smaller(X2,X3,X1)
| ~ rel_str(X2) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_138,plain,
rel_str(esk3_0),
inference(equality_inference,[],[130]) ).
cnf(i_0_139,plain,
~ in(esk6_0,esk5_1(esk6_0)),
inference(equality_inference,[],[131]) ).
cnf(i_0_140,plain,
one_sorted_str(esk9_0),
inference(equality_inference,[],[132]) ).
cnf(i_0_141,plain,
finite(esk7_0),
inference(equality_inference,[],[133]) ).
cnf(i_0_142,plain,
empty_set != esk8_0,
inference(scs_inference,[],[i_0_58,i_0_65,i_0_83]) ).
cnf(i_0_143,plain,
esk6_0 != empty_set,
inference(scs_inference,[],[i_0_117,i_0_115,i_0_58,i_0_65,i_0_83,i_0_82]) ).
cnf(i_0_144,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_145,plain,
relstr_set_smaller(esk9_0,empty_set,esk10_0),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_117,i_0_115,i_0_144,i_0_58,i_0_65,i_0_83,i_0_82,i_0_45]) ).
cnf(i_0_146,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_147,plain,
( ~ element(X1,the_carrier(X2))
| in(esk2_3(X2,X3,X1),X3)
| relstr_set_smaller(X2,X3,X1)
| ~ rel_str(X2) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_148,plain,
relstr_element_smaller(esk9_0,empty_set,esk10_0),
inference(scs_inference,[],[i_0_54,i_0_61,i_0_117,i_0_115,i_0_144,i_0_146,i_0_58,i_0_65,i_0_83,i_0_82,i_0_45,i_0_46]) ).
cnf(i_0_149,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_150,plain,
( ~ element(X1,the_carrier(X2))
| in(esk1_3(X2,X3,X1),X3)
| relstr_element_smaller(X2,X3,X1)
| ~ rel_str(X2) ),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_151,plain,
$false,
inference(scs_inference,[],[i_0_54,i_0_61,i_0_117,i_0_115,i_0_144,i_0_146,i_0_58,i_0_65,i_0_83,i_0_82,i_0_45,i_0_46,i_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU355+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.16/0.33 % Computer : n022.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 02:59:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.41/1.61 % Version : CSE_E---1.7
% 0.41/1.61 % Problem : theBenchmark.p
% 0.41/1.61 % SZS status Theorem for theBenchmark.p
% 0.41/1.61 % SZS output start CNFRefutation
% See solution above
% 0.62/1.82 % Total time : 1.271s
%------------------------------------------------------------------------------