%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU306+1 : 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 : n003.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 05:11:25 PM UTC 2026
% Result : Theorem 0.25s 1.60s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 81
% Syntax : Number of formulae : 194 ( 32 unt; 0 def)
% Number of atoms : 570 ( 69 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 655 ( 279 ~; 257 |; 81 &)
% ( 1 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-1 aty)
% Number of variables : 319 ( 5 sgn 109 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(t12_pre_topc,conjecture,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(rc1_membered,axiom,
? [X1] :
( ~ empty(X1)
& v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(dt_k2_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(cc17_membered,axiom,
! [X1] :
( v2_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
fof(cc18_membered,axiom,
! [X1] :
( v3_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
fof(cc19_membered,axiom,
! [X1] :
( v4_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2)
& v4_membered(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
fof(cc20_membered,axiom,
! [X1] :
( v5_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2)
& v4_membered(X2)
& v5_membered(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
fof(cc16_membered,axiom,
! [X1] :
( v1_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> v1_membered(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(cc14_membered,axiom,
! [X1] :
( v5_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& natural(X2)
& v1_xreal_0(X2)
& v1_int_1(X2)
& v1_rat_1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
fof(cc13_membered,axiom,
! [X1] :
( v4_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2)
& v1_int_1(X2)
& v1_rat_1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
fof(cc12_membered,axiom,
! [X1] :
( v3_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2)
& v1_rat_1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
fof(cc11_membered,axiom,
! [X1] :
( v2_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
fof(cc10_membered,axiom,
! [X1] :
( v1_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> v1_xcmplx_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
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(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(cc15_membered,axiom,
! [X1] :
( empty(X1)
=> ( v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
fof(cc4_membered,axiom,
! [X1] :
( v2_membered(X1)
=> v1_membered(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
fof(cc3_membered,axiom,
! [X1] :
( v3_membered(X1)
=> v2_membered(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
fof(cc2_membered,axiom,
! [X1] :
( v4_membered(X1)
=> v3_membered(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
fof(cc1_membered,axiom,
! [X1] :
( v5_membered(X1)
=> v4_membered(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(existence_l1_struct_0,axiom,
? [X1] : one_sorted_str(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(fc6_membered,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
fof(i_0_35,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_36,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_37,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_38,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
inference(assume_negation,[status(cth)],[t12_pre_topc]) ).
fof(i_0_39,plain,
? [X1] :
( ~ empty(X1)
& v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ),
inference(fof_simplification,[status(thm)],[rc1_membered]) ).
fof(i_0_40,plain,
! [X91,X92,X93] :
( ~ in(X91,X92)
| ~ element(X92,powerset(X93))
| element(X91,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_41,plain,
! [X94,X95,X96] :
( ~ in(X94,X95)
| ~ element(X95,powerset(X96))
| ~ empty(X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_42,plain,
! [X113,X114] :
( ( ~ element(X113,powerset(X114))
| subset(X113,X114) )
& ( ~ subset(X113,X114)
| element(X113,powerset(X114)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_43,plain,
! [X116] :
( ~ one_sorted_str(X116)
| element(cast_as_carrier_subset(X116),powerset(the_carrier(X116))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pre_topc])]) ).
fof(i_0_44,plain,
! [X62,X63] :
( ~ in(X62,X63)
| ~ in(X63,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_35])]) ).
fof(i_0_45,plain,
! [X81,X82] :
( ( v1_membered(X82)
| ~ element(X82,powerset(X81))
| ~ v2_membered(X81) )
& ( v2_membered(X82)
| ~ element(X82,powerset(X81))
| ~ v2_membered(X81) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_membered])])])]) ).
fof(i_0_46,plain,
! [X83,X84] :
( ( v1_membered(X84)
| ~ element(X84,powerset(X83))
| ~ v3_membered(X83) )
& ( v2_membered(X84)
| ~ element(X84,powerset(X83))
| ~ v3_membered(X83) )
& ( v3_membered(X84)
| ~ element(X84,powerset(X83))
| ~ v3_membered(X83) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc18_membered])])])]) ).
fof(i_0_47,plain,
! [X85,X86] :
( ( v1_membered(X86)
| ~ element(X86,powerset(X85))
| ~ v4_membered(X85) )
& ( v2_membered(X86)
| ~ element(X86,powerset(X85))
| ~ v4_membered(X85) )
& ( v3_membered(X86)
| ~ element(X86,powerset(X85))
| ~ v4_membered(X85) )
& ( v4_membered(X86)
| ~ element(X86,powerset(X85))
| ~ v4_membered(X85) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc19_membered])])])]) ).
fof(i_0_48,plain,
! [X87,X88] :
( ( v1_membered(X88)
| ~ element(X88,powerset(X87))
| ~ v5_membered(X87) )
& ( v2_membered(X88)
| ~ element(X88,powerset(X87))
| ~ v5_membered(X87) )
& ( v3_membered(X88)
| ~ element(X88,powerset(X87))
| ~ v5_membered(X87) )
& ( v4_membered(X88)
| ~ element(X88,powerset(X87))
| ~ v5_membered(X87) )
& ( v5_membered(X88)
| ~ element(X88,powerset(X87))
| ~ v5_membered(X87) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc20_membered])])])]) ).
fof(i_0_49,plain,
! [X79,X80] :
( ~ v1_membered(X79)
| ~ element(X80,powerset(X79))
| v1_membered(X80) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc16_membered])])]) ).
fof(i_0_50,plain,
! [X103,X104] :
( ~ element(X103,X104)
| empty(X104)
| in(X103,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_51,plain,
! [X89,X90] :
( ~ in(X89,X90)
| element(X89,X90) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_52,plain,
! [X77,X78] :
( ( v1_xcmplx_0(X78)
| ~ element(X78,X77)
| ~ v5_membered(X77) )
& ( natural(X78)
| ~ element(X78,X77)
| ~ v5_membered(X77) )
& ( v1_xreal_0(X78)
| ~ element(X78,X77)
| ~ v5_membered(X77) )
& ( v1_int_1(X78)
| ~ element(X78,X77)
| ~ v5_membered(X77) )
& ( v1_rat_1(X78)
| ~ element(X78,X77)
| ~ v5_membered(X77) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc14_membered])])])]) ).
fof(i_0_53,plain,
! [X75,X76] :
( ( v1_xcmplx_0(X76)
| ~ element(X76,X75)
| ~ v4_membered(X75) )
& ( v1_xreal_0(X76)
| ~ element(X76,X75)
| ~ v4_membered(X75) )
& ( v1_int_1(X76)
| ~ element(X76,X75)
| ~ v4_membered(X75) )
& ( v1_rat_1(X76)
| ~ element(X76,X75)
| ~ v4_membered(X75) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc13_membered])])])]) ).
fof(i_0_54,plain,
! [X73,X74] :
( ( v1_xcmplx_0(X74)
| ~ element(X74,X73)
| ~ v3_membered(X73) )
& ( v1_xreal_0(X74)
| ~ element(X74,X73)
| ~ v3_membered(X73) )
& ( v1_rat_1(X74)
| ~ element(X74,X73)
| ~ v3_membered(X73) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc12_membered])])])]) ).
fof(i_0_55,plain,
! [X71,X72] :
( ( v1_xcmplx_0(X72)
| ~ element(X72,X71)
| ~ v2_membered(X71) )
& ( v1_xreal_0(X72)
| ~ element(X72,X71)
| ~ v2_membered(X71) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc11_membered])])])]) ).
fof(i_0_56,plain,
! [X69,X70] :
( ~ v1_membered(X69)
| ~ element(X70,X69)
| v1_xcmplx_0(X70) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc10_membered])])]) ).
fof(i_0_57,plain,
! [X98] :
( ( element(esk2_1(X98),powerset(X98))
| empty(X98) )
& ( ~ empty(esk2_1(X98))
| empty(X98) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_36])])])]) ).
fof(i_0_58,plain,
! [X106,X107] :
( ~ in(X106,X107)
| ~ empty(X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_59,plain,
! [X100] :
( element(esk3_1(X100),powerset(X100))
& empty(esk3_1(X100)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_60,plain,
! [X110] : element(esk4_1(X110),X110),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_61,plain,
! [X112] : ~ empty(powerset(X112)),
inference(variable_rename,[status(thm)],[i_0_37]) ).
fof(i_0_62,plain,
! [X108,X109] :
( ~ empty(X108)
| X108 = X109
| ~ empty(X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_63,plain,
! [X117] :
( ~ one_sorted_str(X117)
| cast_as_carrier_subset(X117) = the_carrier(X117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
fof(i_0_64,plain,
! [X97] : subset(X97,X97),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_65,plain,
! [X102] :
( ( v1_membered(X102)
| ~ empty(X102) )
& ( v2_membered(X102)
| ~ empty(X102) )
& ( v3_membered(X102)
| ~ empty(X102) )
& ( v4_membered(X102)
| ~ empty(X102) )
& ( v5_membered(X102)
| ~ empty(X102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc15_membered])])]) ).
fof(i_0_66,plain,
! [X67] :
( ~ v2_membered(X67)
| v1_membered(X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_membered])]) ).
fof(i_0_67,plain,
! [X66] :
( ~ v3_membered(X66)
| v2_membered(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_membered])]) ).
fof(i_0_68,plain,
! [X65] :
( ~ v4_membered(X65)
| v3_membered(X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_membered])]) ).
fof(i_0_69,plain,
! [X64] :
( ~ v5_membered(X64)
| v4_membered(X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_membered])]) ).
fof(i_0_70,plain,
! [X105] :
( ~ empty(X105)
| X105 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_71,negated_conjecture,
( one_sorted_str(esk6_0)
& cast_as_carrier_subset(esk6_0) != the_carrier(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_38])])]) ).
fof(i_0_72,plain,
( ~ empty(esk1_0)
& v1_membered(esk1_0)
& v2_membered(esk1_0)
& v3_membered(esk1_0)
& v4_membered(esk1_0)
& v5_membered(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_39])]) ).
fof(i_0_73,plain,
one_sorted_str(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_struct_0])]) ).
cnf(i_0_74,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_75,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_76,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_77,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_78,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_79,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_80,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_81,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_82,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_83,plain,
( v1_membered(X2)
| ~ v1_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_84,plain,
( v2_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_85,plain,
( v2_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_86,plain,
( v2_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_87,plain,
( v2_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_88,plain,
( v3_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_89,plain,
( v3_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_90,plain,
( v3_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_91,plain,
( v4_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_92,plain,
( v4_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_93,plain,
( v5_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_94,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_95,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_96,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_97,plain,
( natural(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_98,plain,
( v1_int_1(X1)
| ~ element(X1,X2)
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_99,plain,
( v1_int_1(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_100,plain,
( v1_rat_1(X1)
| ~ element(X1,X2)
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_101,plain,
( v1_rat_1(X1)
| ~ element(X1,X2)
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_102,plain,
( v1_rat_1(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_103,plain,
( v1_xreal_0(X1)
| ~ element(X1,X2)
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_104,plain,
( v1_xreal_0(X1)
| ~ element(X1,X2)
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_105,plain,
( v1_xreal_0(X1)
| ~ element(X1,X2)
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_106,plain,
( v1_xreal_0(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_107,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_108,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_109,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_110,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_111,plain,
( v1_xcmplx_0(X2)
| ~ v1_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_112,plain,
( element(esk2_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_113,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_114,plain,
element(esk3_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_115,plain,
( empty(X1)
| ~ empty(esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_116,plain,
element(esk4_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_117,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_118,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_119,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_120,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_121,plain,
( v1_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_122,plain,
( v1_membered(X1)
| ~ v2_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_123,plain,
( v2_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_124,plain,
( v2_membered(X1)
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_125,plain,
( v3_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_126,plain,
( v3_membered(X1)
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_127,plain,
( v4_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_128,plain,
( v4_membered(X1)
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_129,plain,
( v5_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_130,plain,
empty(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_131,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_132,negated_conjecture,
cast_as_carrier_subset(esk6_0) != the_carrier(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_133,plain,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_134,negated_conjecture,
one_sorted_str(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_135,plain,
one_sorted_str(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_136,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_137,plain,
v1_membered(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_138,plain,
v1_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_139,plain,
v2_membered(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_140,plain,
v2_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_141,plain,
v3_membered(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_142,plain,
v3_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_143,plain,
v4_membered(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_144,plain,
v4_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_145,plain,
v5_membered(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_146,plain,
v5_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_147,axiom,
X1 = X1 ).
cnf(i_0_148,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_149,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_150,axiom,
( X1 != X2
| cast_as_carrier_subset(X1) = cast_as_carrier_subset(X2) ) ).
cnf(i_0_151,axiom,
( X1 != X2
| the_carrier(X1) = the_carrier(X2) ) ).
cnf(i_0_152,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_153,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_154,axiom,
( X1 != X2
| ~ v5_membered(X1)
| v5_membered(X2) ) ).
cnf(i_0_155,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| ~ v1_int_1(X1)
| v1_int_1(X2) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| ~ v1_rat_1(X1)
| v1_rat_1(X2) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| ~ v1_xreal_0(X1)
| v1_xreal_0(X2) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| ~ v1_xcmplx_0(X1)
| v1_xcmplx_0(X2) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_163,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_164,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_165,axiom,
( X1 != X2
| ~ one_sorted_str(X1)
| one_sorted_str(X2) ) ).
cnf(i_0_166,axiom,
( X1 != X2
| ~ v1_membered(X1)
| v1_membered(X2) ) ).
cnf(i_0_167,axiom,
( X1 != X2
| ~ v2_membered(X1)
| v2_membered(X2) ) ).
cnf(i_0_168,axiom,
( X1 != X2
| ~ v3_membered(X1)
| v3_membered(X2) ) ).
cnf(i_0_169,axiom,
( X1 != X2
| ~ v4_membered(X1)
| v4_membered(X2) ) ).
cnf(i_0_147_001,axiom,
X1 = X1 ).
cnf(i_0_148_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_149_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_150_004,axiom,
( X1 != X2
| cast_as_carrier_subset(X1) = cast_as_carrier_subset(X2) ) ).
cnf(i_0_151_005,axiom,
( X1 != X2
| the_carrier(X1) = the_carrier(X2) ) ).
cnf(i_0_152_006,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_153_007,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_154_008,axiom,
( X1 != X2
| ~ v5_membered(X1)
| v5_membered(X2) ) ).
cnf(i_0_155_009,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_156_010,axiom,
( X1 != X2
| ~ v1_int_1(X1)
| v1_int_1(X2) ) ).
cnf(i_0_157_011,axiom,
( X1 != X2
| ~ v1_rat_1(X1)
| v1_rat_1(X2) ) ).
cnf(i_0_158_012,axiom,
( X1 != X2
| ~ v1_xreal_0(X1)
| v1_xreal_0(X2) ) ).
cnf(i_0_159_013,axiom,
( X1 != X2
| ~ v1_xcmplx_0(X1)
| v1_xcmplx_0(X2) ) ).
cnf(i_0_160_014,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_161_015,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_162_016,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_163_017,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_164_018,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_165_019,axiom,
( X1 != X2
| ~ one_sorted_str(X1)
| one_sorted_str(X2) ) ).
cnf(i_0_166_020,axiom,
( X1 != X2
| ~ v1_membered(X1)
| v1_membered(X2) ) ).
cnf(i_0_167_021,axiom,
( X1 != X2
| ~ v2_membered(X1)
| v2_membered(X2) ) ).
cnf(i_0_168_022,axiom,
( X1 != X2
| ~ v3_membered(X1)
| v3_membered(X2) ) ).
cnf(i_0_169_023,axiom,
( X1 != X2
| ~ v4_membered(X1)
| v4_membered(X2) ) ).
cnf(i_0_170,plain,
$false,
inference(scs_inference,[],[i_0_132,i_0_134,i_0_119]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU306+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n003.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:55:56 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.25/1.60 % Version : CSE_E---1.7
% 0.25/1.60 % Problem : theBenchmark.p
% 0.25/1.60 % SZS status Theorem for theBenchmark.p
% 0.25/1.60 % SZS output start CNFRefutation
% See solution above
% 0.25/1.62 % Total time : 1.270s
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