%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV542+1 : TPTP v9.2.1. Released v9.1.0.
% 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 : n002.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 05:15:22 PM UTC 2026
% Result : Theorem 210.43s 97.89s
% Output : CNFRefutation 210.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 138 ( 43 unt; 0 def)
% Number of atoms : 298 ( 27 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 273 ( 113 ~; 122 |; 24 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 259 ( 39 sgn 61 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(atleast2p_def,axiom,
! [X1] :
( atleast2p(X1)
<=> ? [X2] :
( mem(X2,X1)
& ~ subq(X1,p(X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',atleast2p_def) ).
fof(s_ax,axiom,
! [X1,X2] :
( mem(X1,s(X2))
<=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',s_ax) ).
fof(subq_def,axiom,
! [X1,X2] :
( subq(X1,X2)
<=> ! [X3] :
( mem(X3,X1)
=> mem(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',subq_def) ).
fof(e_ax,axiom,
! [X1] : ~ mem(X1,e),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',e_ax) ).
fof(p_ax,axiom,
! [X1,X2] :
( mem(X1,p(X2))
<=> subq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',p_ax) ).
fof(setext,axiom,
! [X1,X2] :
( subq(X1,X2)
=> ( subq(X2,X1)
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',setext) ).
fof(m_ax,axiom,
! [X1,X2,X3] :
( mem(X1,m(X2,X3))
<=> ( mem(X1,X2)
& ~ mem(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',m_ax) ).
fof(disj_def,axiom,
! [X1,X2] :
( disj(X1,X2)
<=> ~ ? [X3] :
( mem(X3,X1)
& mem(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',disj_def) ).
fof(u_ax,axiom,
! [X1,X2,X3] :
( mem(X1,u(X2,X3))
<=> ( mem(X1,X2)
| mem(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',u_ax) ).
fof(atleast3p_def,axiom,
! [X1] :
( atleast3p(X1)
<=> ? [X2] :
( subq(X2,X1)
& atleast2p(X2)
& ~ subq(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',atleast3p_def) ).
fof(atleast3_81,conjecture,
atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast3_81) ).
fof(n_def,axiom,
! [X1] : n(X1) = a(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',n_def) ).
fof(a_def,axiom,
! [X1,X2] : a(X1,X2) = u(X1,s(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',a_def) ).
fof(c_0_13,plain,
! [X1] :
( atleast2p(X1)
<=> ? [X2] :
( mem(X2,X1)
& ~ subq(X1,p(X2)) ) ),
inference(fof_simplification,[status(thm)],[atleast2p_def]) ).
fof(c_0_14,plain,
! [X71,X72] :
( ( ~ mem(X71,s(X72))
| X71 = X72 )
& ( X71 != X72
| mem(X71,s(X72)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s_ax])]) ).
fof(c_0_15,plain,
! [X84,X86,X87] :
( ( mem(esk3_1(X84),X84)
| ~ atleast2p(X84) )
& ( ~ subq(X84,p(esk3_1(X84)))
| ~ atleast2p(X84) )
& ( ~ mem(X87,X86)
| subq(X86,p(X87))
| atleast2p(X86) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])]) ).
fof(c_0_16,plain,
! [X56,X57,X58,X59,X60] :
( ( ~ subq(X56,X57)
| ~ mem(X58,X56)
| mem(X58,X57) )
& ( mem(esk1_2(X59,X60),X59)
| subq(X59,X60) )
& ( ~ mem(esk1_2(X59,X60),X60)
| subq(X59,X60) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subq_def])])])])])]) ).
cnf(c_0_17,plain,
( X1 = X2
| ~ mem(X1,s(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( mem(esk3_1(X1),X1)
| ~ atleast2p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( mem(esk1_2(X1,X2),X1)
| subq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X1] : ~ mem(X1,e),
inference(fof_simplification,[status(thm)],[e_ax]) ).
cnf(c_0_21,plain,
( mem(X1,s(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( ~ subq(X1,p(esk3_1(X1)))
| ~ atleast2p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( esk3_1(s(X1)) = X1
| ~ atleast2p(s(X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( subq(X1,X2)
| ~ mem(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( esk1_2(s(X1),X2) = X1
| subq(s(X1),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
fof(c_0_26,plain,
! [X70] : ~ mem(X70,e),
inference(variable_rename,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( mem(X3,X2)
| ~ subq(X1,X2)
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,plain,
mem(X1,s(X1)),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( subq(X2,p(X1))
| atleast2p(X2)
| ~ mem(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,plain,
( ~ atleast2p(s(X1))
| ~ subq(s(X1),p(X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
( subq(s(X1),X2)
| ~ mem(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_32,plain,
! [X82,X83] :
( ( ~ mem(X82,p(X83))
| subq(X82,X83) )
& ( ~ subq(X82,X83)
| mem(X82,p(X83)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p_ax])]) ).
fof(c_0_33,plain,
! [X62,X63] :
( ~ subq(X62,X63)
| ~ subq(X63,X62)
| X62 = X63 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[setext])]) ).
cnf(c_0_34,plain,
~ mem(X1,e),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( mem(X1,X2)
| ~ subq(s(X1),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
( atleast2p(s(X1))
| subq(s(X1),p(X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_37,plain,
( ~ atleast2p(s(X1))
| ~ mem(X1,p(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( mem(X1,p(X2))
| ~ subq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
subq(X1,X1),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_40,plain,
( X1 = X2
| ~ subq(X1,X2)
| ~ subq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
subq(e,X1),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_42,plain,
( subq(X1,X2)
| ~ mem(X1,p(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,plain,
( atleast2p(s(X1))
| mem(X1,p(X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
~ atleast2p(s(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_45,plain,
( X1 = e
| ~ subq(X1,e) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( subq(esk1_2(p(X1),X2),X1)
| subq(p(X1),X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_19]) ).
fof(c_0_47,plain,
! [X1,X2,X3] :
( mem(X1,m(X2,X3))
<=> ( mem(X1,X2)
& ~ mem(X1,X3) ) ),
inference(fof_simplification,[status(thm)],[m_ax]) ).
cnf(c_0_48,plain,
mem(X1,p(X1)),
inference(sr,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
( subq(X1,p(X2))
| ~ subq(esk1_2(X1,p(X2)),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_38]) ).
cnf(c_0_50,plain,
( esk1_2(p(e),X1) = e
| subq(p(e),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
subq(s(X1),p(X1)),
inference(sr,[status(thm)],[c_0_36,c_0_44]) ).
fof(c_0_52,plain,
! [X76,X77,X78] :
( ( mem(X76,X77)
| ~ mem(X76,m(X77,X78)) )
& ( ~ mem(X76,X78)
| ~ mem(X76,m(X77,X78)) )
& ( ~ mem(X76,X77)
| mem(X76,X78)
| mem(X76,m(X77,X78)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
fof(c_0_53,plain,
! [X64,X65,X66,X67,X68] :
( ( ~ disj(X64,X65)
| ~ mem(X66,X64)
| ~ mem(X66,X65) )
& ( mem(esk2_2(X67,X68),X67)
| disj(X67,X68) )
& ( mem(esk2_2(X67,X68),X68)
| disj(X67,X68) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[disj_def])])])])])]) ).
cnf(c_0_54,plain,
( mem(X1,X2)
| ~ subq(p(X1),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_48]) ).
cnf(c_0_55,plain,
subq(p(e),p(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_41])]) ).
cnf(c_0_56,plain,
( p(X1) = s(X1)
| ~ subq(p(X1),s(X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_57,plain,
( subq(p(e),X1)
| ~ mem(e,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_50]) ).
cnf(c_0_58,plain,
( ~ mem(X1,X2)
| ~ mem(X1,m(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
( mem(esk2_2(X1,X2),X1)
| disj(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( mem(esk2_2(X1,X2),X2)
| disj(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,plain,
mem(e,p(X1)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,plain,
p(e) = s(e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_28])]) ).
cnf(c_0_63,plain,
( mem(X1,X2)
| ~ mem(X1,m(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,plain,
( disj(m(X1,X2),X3)
| ~ mem(esk2_2(m(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( esk2_2(X1,s(X2)) = X2
| disj(X1,s(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_60]) ).
fof(c_0_66,plain,
! [X73,X74,X75] :
( ( ~ mem(X73,u(X74,X75))
| mem(X73,X74)
| mem(X73,X75) )
& ( ~ mem(X73,X74)
| mem(X73,u(X74,X75)) )
& ( ~ mem(X73,X75)
| mem(X73,u(X74,X75)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[u_ax])])]) ).
cnf(c_0_67,plain,
( mem(X1,X2)
| ~ subq(p(X3),X2)
| ~ subq(X1,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_68,plain,
( atleast2p(p(X1))
| subq(p(X1),s(e)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_61]),c_0_62]) ).
cnf(c_0_69,plain,
( mem(esk1_2(m(X1,X2),X3),X1)
| subq(m(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_19]) ).
cnf(c_0_70,plain,
( ~ disj(X1,X2)
| ~ mem(X3,X1)
| ~ mem(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_71,plain,
( disj(m(X1,X2),s(X3))
| ~ mem(X3,X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
( mem(X1,X3)
| mem(X1,m(X2,X3))
| ~ mem(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_73,plain,
( disj(X1,m(X2,X3))
| ~ mem(esk2_2(X1,m(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_58,c_0_60]) ).
cnf(c_0_74,plain,
( mem(X1,u(X3,X2))
| ~ mem(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
( atleast2p(p(X1))
| mem(X2,s(e))
| ~ subq(X2,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_76,plain,
subq(m(X1,X2),X1),
inference(spm,[status(thm)],[c_0_24,c_0_69]) ).
cnf(c_0_77,plain,
( ~ mem(X1,m(X2,X3))
| ~ mem(X1,s(X4))
| ~ mem(X4,X3) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,plain,
( mem(X1,m(p(X1),X2))
| mem(X1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_48]) ).
cnf(c_0_79,plain,
( mem(X1,X2)
| mem(X1,X3)
| ~ mem(X1,u(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_80,plain,
! [X1] :
( atleast3p(X1)
<=> ? [X2] :
( subq(X2,X1)
& atleast2p(X2)
& ~ subq(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[atleast3p_def]) ).
cnf(c_0_81,plain,
( mem(X1,u(X2,X3))
| ~ mem(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_82,plain,
( disj(X1,m(X2,u(X3,X4)))
| ~ mem(esk2_2(X1,m(X2,u(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,plain,
( atleast2p(p(X1))
| mem(m(X1,X2),s(e)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,plain,
( mem(X1,X2)
| ~ mem(X1,s(X3))
| ~ mem(X3,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,plain,
( mem(X1,s(e))
| ~ subq(X1,e) ),
inference(spm,[status(thm)],[c_0_38,c_0_62]) ).
cnf(c_0_86,plain,
( mem(esk1_2(u(X1,X2),X3),X1)
| mem(esk1_2(u(X1,X2),X3),X2)
| subq(u(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_19]) ).
fof(c_0_87,plain,
! [X88,X90,X91] :
( ( subq(esk4_1(X88),X88)
| ~ atleast3p(X88) )
& ( atleast2p(esk4_1(X88))
| ~ atleast3p(X88) )
& ( ~ subq(X88,esk4_1(X88))
| ~ atleast3p(X88) )
& ( ~ subq(X91,X90)
| ~ atleast2p(X91)
| subq(X90,X91)
| atleast3p(X90) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])])])])])]) ).
cnf(c_0_88,plain,
( subq(X1,u(X2,X3))
| ~ mem(esk1_2(X1,u(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_81]) ).
cnf(c_0_89,plain,
disj(X1,m(X2,u(X3,X1))),
inference(spm,[status(thm)],[c_0_82,c_0_59]) ).
cnf(c_0_90,plain,
( mem(X1,m(s(X1),X2))
| mem(X1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_28]) ).
cnf(c_0_91,plain,
( m(X1,X2) = e
| atleast2p(p(X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_83]) ).
cnf(c_0_92,plain,
( mem(X1,X2)
| ~ mem(e,X2)
| ~ subq(X1,e) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
fof(c_0_93,negated_conjecture,
~ atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[atleast3_81])]) ).
fof(c_0_94,plain,
! [X81] : n(X81) = a(X81,X81),
inference(variable_rename,[status(thm)],[n_def]) ).
fof(c_0_95,plain,
! [X79,X80] : a(X79,X80) = u(X79,s(X80)),
inference(variable_rename,[status(thm)],[a_def]) ).
cnf(c_0_96,plain,
( mem(esk1_2(u(X1,X2),X2),X1)
| subq(u(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_86]) ).
cnf(c_0_97,plain,
( subq(X1,u(X2,X3))
| ~ mem(esk1_2(X1,u(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_74]) ).
cnf(c_0_98,plain,
( subq(X2,X1)
| atleast3p(X2)
| ~ subq(X1,X2)
| ~ atleast2p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_99,plain,
subq(X1,u(X1,X2)),
inference(spm,[status(thm)],[c_0_88,c_0_19]) ).
cnf(c_0_100,plain,
( ~ mem(X1,m(X2,u(X3,X4)))
| ~ mem(X1,X4) ),
inference(spm,[status(thm)],[c_0_70,c_0_89]) ).
cnf(c_0_101,plain,
( atleast2p(p(s(X1)))
| mem(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_34]) ).
cnf(c_0_102,plain,
( mem(X1,p(X2))
| ~ subq(X1,e) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_38]),c_0_41])]) ).
cnf(c_0_103,negated_conjecture,
~ atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_104,plain,
n(X1) = a(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_105,plain,
a(X1,X2) = u(X1,s(X2)),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_106,plain,
subq(u(e,X1),X1),
inference(spm,[status(thm)],[c_0_34,c_0_96]) ).
cnf(c_0_107,plain,
subq(X1,u(X2,X1)),
inference(spm,[status(thm)],[c_0_97,c_0_19]) ).
cnf(c_0_108,plain,
( atleast3p(u(X1,X2))
| subq(u(X1,X2),X1)
| ~ atleast2p(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_109,plain,
atleast2p(p(s(X1))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_101]) ).
cnf(c_0_110,plain,
( subq(X1,X2)
| ~ subq(X1,e) ),
inference(spm,[status(thm)],[c_0_42,c_0_102]) ).
cnf(c_0_111,plain,
( disj(X1,p(X2))
| subq(esk2_2(X1,p(X2)),X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_60]) ).
cnf(c_0_112,negated_conjecture,
~ atleast3p(u(p(s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104]),c_0_104]),c_0_104]),c_0_105]),c_0_105]),c_0_105]),c_0_105]),c_0_105]) ).
cnf(c_0_113,plain,
u(e,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_106]),c_0_107])]) ).
cnf(c_0_114,plain,
( atleast3p(u(p(s(X1)),X2))
| subq(u(p(s(X1)),X2),p(s(X1))) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_115,plain,
( disj(m(X1,p(X2)),X3)
| ~ subq(esk2_2(m(X1,p(X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_38]) ).
cnf(c_0_116,plain,
( disj(X1,s(e))
| subq(esk2_2(X1,s(e)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_62]),c_0_62]) ).
cnf(c_0_117,plain,
( esk2_2(s(X1),X2) = X1
| disj(s(X1),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_59]) ).
cnf(c_0_118,negated_conjecture,
~ atleast3p(u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113]),c_0_113]),c_0_113]) ).
cnf(c_0_119,plain,
( u(p(s(X1)),X2) = p(s(X1))
| atleast3p(u(p(s(X1)),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_114]),c_0_99])]) ).
cnf(c_0_120,plain,
disj(m(X1,p(X2)),s(e)),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_121,plain,
( mem(e,X1)
| ~ subq(p(X2),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_61]) ).
cnf(c_0_122,plain,
( disj(s(X1),s(e))
| subq(X1,X2) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_123,plain,
mem(X1,u(X2,s(X1))),
inference(spm,[status(thm)],[c_0_35,c_0_107]) ).
cnf(c_0_124,negated_conjecture,
u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e)))))) = p(s(s(s(e)))),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_125,plain,
( ~ mem(X1,m(X2,p(X3)))
| ~ mem(X1,s(e)) ),
inference(spm,[status(thm)],[c_0_70,c_0_120]) ).
cnf(c_0_126,plain,
( disj(s(p(X1)),s(e))
| mem(e,X2) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_127,plain,
mem(X1,u(s(X1),X2)),
inference(spm,[status(thm)],[c_0_35,c_0_99]) ).
cnf(c_0_128,negated_conjecture,
mem(u(s(s(e)),s(s(s(e)))),p(s(s(s(e))))),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_129,plain,
disj(s(p(X1)),s(e)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_28])]) ).
cnf(c_0_130,plain,
( mem(X1,X2)
| ~ subq(u(s(X1),X3),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_127]) ).
cnf(c_0_131,negated_conjecture,
subq(u(s(s(e)),s(s(s(e)))),s(s(s(e)))),
inference(spm,[status(thm)],[c_0_42,c_0_128]) ).
cnf(c_0_132,plain,
( ~ mem(X1,s(p(X2)))
| ~ mem(X1,s(e)) ),
inference(spm,[status(thm)],[c_0_70,c_0_129]) ).
cnf(c_0_133,negated_conjecture,
mem(s(e),s(s(s(e)))),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_134,plain,
~ mem(p(X1),s(e)),
inference(spm,[status(thm)],[c_0_132,c_0_28]) ).
cnf(c_0_135,negated_conjecture,
s(s(e)) = s(e),
inference(spm,[status(thm)],[c_0_17,c_0_133]) ).
cnf(c_0_136,plain,
~ mem(s(e),s(e)),
inference(spm,[status(thm)],[c_0_134,c_0_62]) ).
cnf(c_0_137,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_135]),c_0_135]),c_0_136]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV542+1 : TPTP v9.2.1. Released v9.1.0.
% 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
% 0.16/0.33 % Computer : n002.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 04:00:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 210.43/97.89 % Version : CSE_E---1.7
% 210.43/97.89 % Problem : theBenchmark.p
% 210.43/97.89 % SZS status Theorem for theBenchmark.p
% 210.43/97.89 % SZS output start CNFRefutation
% See solution above
% 210.93/98.30 % Total time : 82.483s
%------------------------------------------------------------------------------