%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV540+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:35:14 PM UTC 2026
% Result : Theorem 24.39s 3.60s
% Output : CNFRefutation 24.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 122 ( 39 unt; 0 def)
% Number of atoms : 271 ( 39 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 239 ( 90 ~; 111 |; 24 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 9 ( 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 : 207 ( 25 sgn 61 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_ax,axiom,
! [X1] : ~ mem(X1,e),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',e_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(setext,axiom,
! [X1,X2] :
( subq(X1,X2)
=> ( subq(X2,X1)
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',setext) ).
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(s_ax,axiom,
! [X1,X2] :
( mem(X1,s(X2))
<=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',s_ax) ).
fof(u_ax,axiom,
! [X1,X2,X3] :
( mem(X1,u(X2,X3))
<=> ( mem(X1,X3)
| mem(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',u_ax) ).
fof(atleast3_83,conjecture,
atleast3p(u(s(n(e)),a(p(s(s(n(e)))),n(s(n(e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast3_83) ).
fof(atleast3p_def,axiom,
! [X1] :
( atleast3p(X1)
<=> ? [X2] :
( ~ subq(X1,X2)
& atleast2p(X2)
& subq(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',atleast3p_def) ).
fof(atleast2p_def,axiom,
! [X1] :
( atleast2p(X1)
<=> ? [X2] :
( ~ subq(X1,p(X2))
& mem(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',atleast2p_def) ).
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(disj_def,axiom,
! [X1,X2] :
( disj(X1,X2)
<=> ~ ? [X3] :
( mem(X3,X2)
& mem(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',disj_def) ).
fof(m_ax,axiom,
! [X1,X2,X3] :
( mem(X1,m(X2,X3))
<=> ( ~ mem(X1,X3)
& mem(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',m_ax) ).
fof(c_0_13,plain,
! [X1] : ~ mem(X1,e),
inference(fof_simplification,[status(thm)],[e_ax]) ).
fof(c_0_14,plain,
! [X18] : ~ mem(X18,e),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_13])]) ).
fof(c_0_15,plain,
! [X4,X5,X6,X7,X8] :
( ( subq(X7,X8)
| ~ mem(esk1_2(X7,X8),X8) )
& ( subq(X7,X8)
| mem(esk1_2(X7,X8),X7) )
& ( mem(X6,X5)
| ~ mem(X6,X4)
| ~ subq(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).
fof(c_0_16,plain,
! [X10,X11] :
( X10 = X11
| ~ subq(X11,X10)
| ~ subq(X10,X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[setext])])]) ).
cnf(c_0_17,plain,
~ mem(X1,e),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( subq(X1,X2)
| mem(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X30,X31] :
( ( mem(X30,p(X31))
| ~ subq(X30,X31) )
& ( subq(X30,X31)
| ~ mem(X30,p(X31)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p_ax])])]) ).
cnf(c_0_20,plain,
( ~ subq(X2,X1)
| ~ subq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
subq(e,X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ mem(X1,p(X2))
| subq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X19,X20] :
( ( mem(X19,s(X20))
| X19 != X20 )
& ( X19 = X20
| ~ mem(X19,s(X20)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s_ax])])]) ).
fof(c_0_24,plain,
! [X21,X22,X23] :
( ( mem(X21,u(X22,X23))
| ~ mem(X21,X23) )
& ( mem(X21,u(X22,X23))
| ~ mem(X21,X22) )
& ( mem(X21,X23)
| mem(X21,X22)
| ~ mem(X21,u(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[u_ax])])])]) ).
cnf(c_0_25,plain,
( ~ subq(X1,e)
| X1 = e ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( subq(p(X1),X2)
| subq(esk1_2(p(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_27,plain,
( ~ mem(X1,s(X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( ~ mem(esk1_2(X1,X2),X2)
| subq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_29,negated_conjecture,
~ atleast3p(u(s(n(e)),a(p(s(s(n(e)))),n(s(n(e)))))),
inference(assume_negation,[status(cth)],[atleast3_83]) ).
fof(c_0_30,plain,
! [X1] :
( atleast3p(X1)
<=> ? [X2] :
( ~ subq(X1,X2)
& atleast2p(X2)
& subq(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[atleast3p_def]) ).
cnf(c_0_31,plain,
( ~ mem(X1,X2)
| mem(X1,u(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( ~ mem(X1,u(X2,X3))
| mem(X1,X3)
| mem(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( subq(p(e),X1)
| esk1_2(p(e),X1) = e ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
( X1 != X2
| mem(X1,s(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_35,plain,
( subq(s(X1),X2)
| esk1_2(s(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_36,plain,
( ~ subq(X1,X2)
| mem(X1,p(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,plain,
subq(X1,X1),
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
fof(c_0_38,negated_conjecture,
~ atleast3p(u(s(n(e)),a(p(s(s(n(e)))),n(s(n(e)))))),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_39,plain,
! [X36,X38,X39] :
( ( atleast3p(X38)
| subq(X38,X39)
| ~ atleast2p(X39)
| ~ subq(X39,X38) )
& ( ~ atleast3p(X36)
| ~ subq(X36,esk4_1(X36)) )
& ( ~ atleast3p(X36)
| atleast2p(esk4_1(X36)) )
& ( ~ atleast3p(X36)
| subq(esk4_1(X36),X36) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_30])])])])])])]) ).
cnf(c_0_40,plain,
( subq(X1,X2)
| mem(esk1_2(X1,X2),u(X3,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_18]) ).
cnf(c_0_41,plain,
( subq(u(X1,X2),X3)
| mem(esk1_2(u(X1,X2),X3),X2)
| mem(esk1_2(u(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
fof(c_0_42,plain,
! [X1] :
( atleast2p(X1)
<=> ? [X2] :
( ~ subq(X1,p(X2))
& mem(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[atleast2p_def]) ).
cnf(c_0_43,plain,
( ~ mem(e,X1)
| subq(p(e),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_44,plain,
mem(X1,s(X1)),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_45,plain,
( ~ mem(X1,X2)
| subq(s(X1),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_46,plain,
mem(X1,p(X1)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_47,negated_conjecture,
~ atleast3p(u(s(n(e)),a(p(s(s(n(e)))),n(s(n(e)))))),
inference(fof_nnf,[status(thm)],[c_0_38]) ).
fof(c_0_48,plain,
! [X29] : n(X29) = a(X29,X29),
inference(variable_rename,[status(thm)],[n_def]) ).
fof(c_0_49,plain,
! [X27,X28] : a(X27,X28) = u(X27,s(X28)),
inference(variable_rename,[status(thm)],[a_def]) ).
cnf(c_0_50,plain,
( ~ atleast2p(X1)
| ~ subq(X1,X2)
| atleast3p(X2)
| subq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_51,plain,
subq(X1,u(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_52,plain,
( subq(u(X1,X2),X2)
| mem(esk1_2(u(X1,X2),X2),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_41]) ).
fof(c_0_53,plain,
! [X32,X34,X35] :
( ( atleast2p(X34)
| subq(X34,p(X35))
| ~ mem(X35,X34) )
& ( ~ atleast2p(X32)
| ~ subq(X32,p(esk3_1(X32))) )
& ( ~ atleast2p(X32)
| mem(esk3_1(X32),X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_42])])])])])])]) ).
cnf(c_0_54,plain,
( ~ mem(X1,X2)
| mem(X1,u(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_55,plain,
subq(p(e),s(e)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_56,plain,
subq(s(X1),p(X1)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
~ atleast3p(u(s(n(e)),a(p(s(s(n(e)))),n(s(n(e)))))),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,plain,
n(X1) = a(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,plain,
a(X1,X2) = u(X1,s(X2)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,plain,
( ~ atleast2p(X2)
| subq(u(X1,X2),X2)
| atleast3p(u(X1,X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_61,plain,
subq(u(e,X1),X1),
inference(spm,[status(thm)],[c_0_17,c_0_52]) ).
cnf(c_0_62,plain,
( ~ mem(X1,X2)
| atleast2p(X2)
| subq(X2,p(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
mem(X1,u(p(X1),X2)),
inference(spm,[status(thm)],[c_0_54,c_0_46]) ).
cnf(c_0_64,plain,
( subq(X1,X2)
| mem(esk1_2(X1,X2),u(X1,X3)) ),
inference(spm,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_65,plain,
p(e) = s(e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_55]),c_0_56])]) ).
fof(c_0_66,plain,
! [X12,X13,X14,X15,X16] :
( ( disj(X15,X16)
| mem(esk2_2(X15,X16),X16) )
& ( disj(X15,X16)
| mem(esk2_2(X15,X16),X15) )
& ( ~ mem(X14,X13)
| ~ mem(X14,X12)
| ~ disj(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_67,negated_conjecture,
~ atleast3p(u(s(u(e,s(e))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_58]),c_0_58]),c_0_58]),c_0_59]),c_0_59]),c_0_59]),c_0_59]),c_0_59]),c_0_59]) ).
cnf(c_0_68,plain,
( ~ atleast2p(X2)
| atleast3p(u(X1,X2))
| u(X1,X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_60]),c_0_51])]) ).
cnf(c_0_69,plain,
u(e,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_61]),c_0_51])]) ).
cnf(c_0_70,plain,
( subq(u(p(X1),X2),p(X1))
| atleast2p(u(p(X1),X2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
subq(X1,u(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_64]) ).
cnf(c_0_72,plain,
( ~ mem(X3,X1)
| ~ subq(X1,X2)
| mem(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_73,plain,
( ~ mem(X1,s(e))
| subq(X1,e) ),
inference(spm,[status(thm)],[c_0_22,c_0_65]) ).
cnf(c_0_74,plain,
( disj(X1,X2)
| mem(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_75,plain,
! [X1,X2,X3] :
( mem(X1,m(X2,X3))
<=> ( ~ mem(X1,X3)
& mem(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[m_ax]) ).
cnf(c_0_76,negated_conjecture,
( ~ atleast2p(u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e)))))))
| u(s(s(e)),u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e))))))) = 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)],[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(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_69]),c_0_69]) ).
cnf(c_0_77,plain,
( atleast2p(u(p(X1),X2))
| u(p(X1),X2) = p(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_70]),c_0_71])]) ).
cnf(c_0_78,plain,
mem(e,p(X1)),
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_79,plain,
( ~ subq(X1,X3)
| subq(X1,X2)
| mem(esk1_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_72,c_0_18]) ).
cnf(c_0_80,plain,
( subq(esk2_2(X1,s(e)),e)
| disj(X1,s(e)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,plain,
( disj(X1,X2)
| mem(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_82,plain,
! [X24,X25,X26] :
( ( mem(X24,m(X25,X26))
| mem(X24,X26)
| ~ mem(X24,X25) )
& ( ~ mem(X24,m(X25,X26))
| ~ mem(X24,X26) )
& ( ~ mem(X24,m(X25,X26))
| mem(X24,X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])]) ).
cnf(c_0_83,negated_conjecture,
~ atleast3p(u(s(s(e)),u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e)))))))),
inference(spm,[status(thm)],[c_0_67,c_0_69]) ).
cnf(c_0_84,negated_conjecture,
( u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e)))))) = p(s(s(s(e))))
| u(s(s(e)),u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e))))))) = u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e)))))) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_85,plain,
( ~ atleast2p(X1)
| subq(u(X1,X2),X1)
| atleast3p(u(X1,X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_71]) ).
cnf(c_0_86,plain,
( subq(p(X1),p(e))
| atleast2p(p(X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_78]) ).
cnf(c_0_87,plain,
( subq(esk2_2(X1,s(e)),X2)
| disj(X1,s(e)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_17]) ).
cnf(c_0_88,plain,
( disj(s(X1),X2)
| esk2_2(s(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_81]) ).
cnf(c_0_89,plain,
( ~ mem(X1,m(X2,X3))
| mem(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( ~ atleast3p(u(p(s(s(s(e)))),s(u(s(s(e)),s(s(s(e)))))))
| 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_83,c_0_84]) ).
cnf(c_0_91,plain,
( ~ atleast2p(X1)
| atleast3p(u(X1,X2))
| u(X1,X2) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_85]),c_0_71])]) ).
cnf(c_0_92,plain,
( ~ subq(p(e),p(X1))
| atleast2p(p(X1))
| p(e) = p(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_86]) ).
cnf(c_0_93,plain,
subq(p(e),p(X1)),
inference(spm,[status(thm)],[c_0_43,c_0_78]) ).
cnf(c_0_94,plain,
( subq(X1,X2)
| disj(s(X1),s(e)) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,plain,
( subq(m(X1,X2),X3)
| mem(esk1_2(m(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_18]) ).
cnf(c_0_96,negated_conjecture,
( ~ atleast2p(p(s(s(s(e)))))
| 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_90,c_0_91]) ).
cnf(c_0_97,plain,
( atleast2p(p(X1))
| p(X1) = s(e) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]),c_0_65]) ).
cnf(c_0_98,plain,
( ~ mem(X1,m(X3,X2))
| ~ mem(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_99,plain,
mem(X1,p(u(X1,X2))),
inference(spm,[status(thm)],[c_0_36,c_0_71]) ).
cnf(c_0_100,plain,
( ~ subq(X1,X2)
| disj(s(X2),s(e))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_20,c_0_94]) ).
cnf(c_0_101,plain,
subq(m(X1,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_95]) ).
cnf(c_0_102,negated_conjecture,
( p(s(s(s(e)))) = s(e)
| 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_96,c_0_97]) ).
cnf(c_0_103,plain,
~ mem(X1,m(X2,p(u(X1,X3)))),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,plain,
( disj(s(X1),s(e))
| m(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,plain,
( disj(X1,s(X2))
| esk2_2(X1,s(X2)) = X2 ),
inference(spm,[status(thm)],[c_0_27,c_0_74]) ).
cnf(c_0_106,plain,
mem(X1,u(s(X1),X2)),
inference(spm,[status(thm)],[c_0_54,c_0_44]) ).
cnf(c_0_107,negated_conjecture,
( p(s(s(s(e)))) = s(e)
| u(s(s(e)),p(s(s(s(e))))) = p(s(s(s(e)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_102]),c_0_97]) ).
cnf(c_0_108,plain,
( ~ mem(X2,X1)
| disj(s(X1),s(e)) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,plain,
( ~ mem(X3,X2)
| ~ mem(X3,X1)
| ~ disj(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_110,plain,
( mem(X2,X1)
| disj(X1,s(X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( mem(s(e),p(s(s(s(e)))))
| p(s(s(s(e)))) = s(e) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,plain,
disj(s(s(X1)),s(e)),
inference(spm,[status(thm)],[c_0_108,c_0_44]) ).
cnf(c_0_113,plain,
( ~ mem(X3,X2)
| ~ mem(X3,s(X1))
| mem(X1,X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,negated_conjecture,
( subq(s(e),s(s(s(e))))
| p(s(s(s(e)))) = s(e) ),
inference(spm,[status(thm)],[c_0_22,c_0_111]) ).
cnf(c_0_115,plain,
( ~ mem(X1,s(e))
| ~ mem(X1,s(s(X2))) ),
inference(spm,[status(thm)],[c_0_109,c_0_112]) ).
cnf(c_0_116,plain,
( ~ mem(X2,s(X1))
| mem(X1,s(X2)) ),
inference(spm,[status(thm)],[c_0_113,c_0_44]) ).
cnf(c_0_117,negated_conjecture,
( subq(s(e),s(s(s(e))))
| mem(s(s(s(e))),s(e)) ),
inference(spm,[status(thm)],[c_0_46,c_0_114]) ).
cnf(c_0_118,plain,
~ mem(e,s(s(X1))),
inference(spm,[status(thm)],[c_0_115,c_0_44]) ).
cnf(c_0_119,plain,
( ~ subq(s(X1),X2)
| mem(X1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_44]) ).
cnf(c_0_120,negated_conjecture,
subq(s(e),s(s(s(e)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]) ).
cnf(c_0_121,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_118]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV540+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.41 % Computer : n013.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Mon Sep 21 07:24:35 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.39/3.60 % Version: 3.5.1
% 24.39/3.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 24.39/3.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.39/3.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 24.39/3.60 % Starting new_bool_3 with 300s (1) cores
% 24.39/3.60 % Starting new_bool_1 with 300s (1) cores
% 24.39/3.60 % Starting sh5l with 300s (1) cores
% 24.39/3.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 268520 completed with status 0
% 24.39/3.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 24.39/3.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 24.39/3.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.39/3.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 24.39/3.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.39/3.60 % No SInE strategy applied
% 24.39/3.60 % Search class: FGHSF-FFMF21-DFFFFFNN
% 24.39/3.60 % partial match(1): FGHSF-FFMF21-SFFFFFNN
% 24.39/3.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 24.39/3.60 % Starting SubtermCWHack with 136s (1) cores
% 24.39/3.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 24.39/3.60 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 24.39/3.60 % Starting new_bool_3 with 136s (1) cores
% 24.39/3.60 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N with 136s (1) cores
% 24.39/3.60 % new_bool_3 with pid 268530 completed with status 0
% 24.39/3.60 % Result found by new_bool_3
% 24.39/3.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 24.39/3.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.39/3.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 24.39/3.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.39/3.60 % No SInE strategy applied
% 24.39/3.60 % Search class: FGHSF-FFMF21-DFFFFFNN
% 24.39/3.60 % partial match(1): FGHSF-FFMF21-SFFFFFNN
% 24.39/3.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 24.39/3.60 % Starting SubtermCWHack with 136s (1) cores
% 24.39/3.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 24.39/3.60 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 24.39/3.60 % Starting new_bool_3 with 136s (1) cores
% 24.39/3.60 % Preprocessing time : 0.002 s
% 24.39/3.60 % Presaturation interreduction done
% 24.39/3.60
% 24.39/3.60 % Proof found!
% 24.39/3.60 % SZS status Theorem
% 24.39/3.60 % SZS output start CNFRefutation
% See solution above
% 24.39/3.61 % Parsed axioms : 26
% 24.39/3.61 % Removed by relevancy pruning/SinE : 0
% 24.39/3.61 % Initial clauses : 80
% 24.39/3.61 % Removed in clause preprocessing : 2
% 24.39/3.61 % Initial clauses in saturation : 78
% 24.39/3.61 % Processed clauses : 19812
% 24.39/3.61 % ...of these trivial : 945
% 24.39/3.61 % ...subsumed : 12828
% 24.39/3.61 % ...remaining for further processing : 6039
% 24.39/3.61 % Other redundant clauses eliminated : 1
% 24.39/3.61 % Clauses deleted for lack of memory : 0
% 24.39/3.61 % Backward-subsumed : 695
% 24.39/3.61 % Backward-rewritten : 278
% 24.39/3.61 % Generated clauses : 126707
% 24.39/3.61 % ...of the previous two non-redundant : 100572
% 24.39/3.61 % ...aggressively subsumed : 0
% 24.39/3.61 % Contextual simplify-reflections : 205
% 24.39/3.61 % Paramodulations : 126663
% 24.39/3.61 % Factorizations : 40
% 24.39/3.61 % NegExts : 0
% 24.39/3.61 % Equation resolutions : 1
% 24.39/3.61 % Disequality decompositions : 0
% 24.39/3.61 % Total rewrite steps : 30953
% 24.39/3.61 % ...of those cached : 24872
% 24.39/3.61 % Propositional unsat checks : 1
% 24.39/3.61 % Propositional check models : 0
% 24.39/3.61 % Propositional check unsatisfiable : 0
% 24.39/3.61 % Propositional clauses : 0
% 24.39/3.61 % Propositional clauses after purity: 0
% 24.39/3.61 % Propositional unsat core size : 0
% 24.39/3.61 % Propositional preprocessing time : 0.000
% 24.39/3.61 % Propositional encoding time : 0.083
% 24.39/3.61 % Propositional solver time : 0.067
% 24.39/3.61 % Success case prop preproc time : 0.000
% 24.39/3.61 % Success case prop encoding time : 0.000
% 24.39/3.61 % Success case prop solver time : 0.000
% 24.39/3.61 % Current number of processed clauses : 4984
% 24.39/3.61 % Positive orientable unit clauses : 714
% 24.39/3.61 % Positive unorientable unit clauses: 0
% 24.39/3.61 % Negative unit clauses : 614
% 24.39/3.61 % Non-unit-clauses : 3656
% 24.39/3.61 % Current number of unprocessed clauses: 78424
% 24.39/3.61 % ...number of literals in the above : 215715
% 24.39/3.61 % Current number of archived formulas : 0
% 24.39/3.61 % Current number of archived clauses : 1056
% 24.39/3.61 % Clause-clause subsumption calls (NU) : 2784431
% 24.39/3.61 % Rec. Clause-clause subsumption calls : 1512364
% 24.39/3.61 % Non-unit clause-clause subsumptions : 7521
% 24.39/3.61 % Unit Clause-clause subsumption calls : 481523
% 24.39/3.61 % Rewrite failures with RHS unbound : 0
% 24.39/3.61 % BW rewrite match attempts : 28442
% 24.39/3.61 % BW rewrite match successes : 142
% 24.39/3.61 % Condensation attempts : 0
% 24.39/3.61 % Condensation successes : 0
% 24.39/3.61 % Termbank termtop insertions : 2410788
% 24.39/3.61 % Search garbage collected termcells : 1295
% 24.39/3.61
% 24.39/3.61 % -------------------------------------------------
% 24.39/3.61 % User time : 2.924 s
% 24.39/3.61 % System time : 0.088 s
% 24.39/3.61 % Total time : 3.012 s
% 24.39/3.61 % Maximum resident set size: 3416 pages
% 24.39/3.61
% 24.39/3.61 % -------------------------------------------------
% 24.39/3.61 % User time : 14.415 s
% 24.39/3.61 % System time : 0.451 s
% 24.39/3.61 % Total time : 14.866 s
% 24.39/3.61 % Maximum resident set size: 4864 pages
% 24.39/3.61 % E exiting
%------------------------------------------------------------------------------