%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT071-1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n011.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 05:05:56 PM UTC 2026
% Result : Unsatisfiable 4.85s 3.46s
% Output : CNFRefutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 14 unt; 0 nHn; 28 RR)
% Number of literals : 66 ( 15 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-5 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-5 aty)
% Number of variables : 95 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_that_0,axiom,
( v_thesis____
| c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_atLeast0LessThan_0,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_SetInterval_Oord__class_OlessThan(X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast0LessThan_0) ).
cnf(cls_bij__betw__def_0,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Obij__betw(X1,X2,X5,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).
cnf(cls_bij__betw__inv__into_0,axiom,
( c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X1,X4,X3)
| ~ c_Fun_Obij__betw(X2,X1,X5,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__inv__into_0) ).
cnf(cls_finite_0,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
cnf(cls_bij__betw__def_1,axiom,
( c_Set_Oimage(X1,X2,X3,X4) = X5
| ~ c_Fun_Obij__betw(X1,X2,X5,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_1) ).
cnf(cls_finite__imageD_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
cnf(cls_inj__on__inverseI_1,axiom,
( c_Fun_Oinj__on(X2,X3,X4,X5)
| hAPP(X1,hAPP(X2,c_ATP__Linkup_Osko__Fun__Xinj__on__inverseI__1__1(X3,X2,X1,X4,X5))) != c_ATP__Linkup_Osko__Fun__Xinj__on__inverseI__1__1(X3,X2,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__inverseI_1) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_ex__bij__betw__nat__finite_0,axiom,
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1(X1,X2),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat),X1,tc_nat,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__bij__betw__nat__finite_0) ).
cnf(c_0_12,axiom,
( v_thesis____
| c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
cls_that_0 ).
cnf(c_0_13,negated_conjecture,
~ v_thesis____,
cls_conjecture_0 ).
cnf(c_0_14,plain,
( c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(sr,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_SetInterval_Oord__class_OlessThan(X1,tc_nat),
cls_atLeast0LessThan_0 ).
cnf(c_0_16,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Obij__betw(X1,X2,X5,X3,X4) ),
cls_bij__betw__def_0 ).
cnf(c_0_17,axiom,
( c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X1,X4,X3)
| ~ c_Fun_Obij__betw(X2,X1,X5,X3,X4) ),
cls_bij__betw__inv__into_0 ).
cnf(c_0_18,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
cls_finite_0 ).
cnf(c_0_19,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
clsarity_bool__Finite__Set_Ofinite_Ofinite ).
cnf(c_0_20,plain,
( c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OlessThan(c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X4,X3)
| ~ c_Fun_Obij__betw(X2,X1,X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
( c_Set_Oimage(X1,X2,X3,X4) = X5
| ~ c_Fun_Obij__betw(X1,X2,X5,X3,X4) ),
cls_bij__betw__def_1 ).
cnf(c_0_23,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
cls_finite__imageD_0 ).
cnf(c_0_24,plain,
c_Finite__Set_Ofinite(X1,tc_bool),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,axiom,
( c_Fun_Oinj__on(X2,X3,X4,X5)
| hAPP(X1,hAPP(X2,c_ATP__Linkup_Osko__Fun__Xinj__on__inverseI__1__1(X3,X2,X1,X4,X5))) != c_ATP__Linkup_Osko__Fun__Xinj__on__inverseI__1__1(X3,X2,X1,X4,X5) ),
cls_inj__on__inverseI_1 ).
cnf(c_0_26,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_27,plain,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X2,tc_nat,tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) != c_SetInterval_Oord__class_OlessThan(c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat)
| ~ c_Fun_Obij__betw(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_nat,tc_Arrow__Order__Mirabelle_Oindi) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X4,X3) = X1
| ~ c_Fun_Obij__betw(X2,X1,X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_29,axiom,
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1(X1,X2),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat),X1,tc_nat,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
cls_ex__bij__betw__nat__finite_0 ).
cnf(c_0_30,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2,X3,X4),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( X1 != c_SetInterval_Oord__class_OlessThan(c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat)
| ~ c_Fun_Obij__betw(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_nat,tc_Arrow__Order__Mirabelle_Oindi) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1(X1,X2),c_SetInterval_Oord__class_OlessThan(c_Finite__Set_Ocard(X1,X2),tc_nat),X1,tc_nat,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rw,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_34,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
~ c_Fun_Obij__betw(X1,c_SetInterval_Oord__class_OlessThan(c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_nat,tc_Arrow__Order__Mirabelle_Oindi),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1(X1,X2),c_SetInterval_Oord__class_OlessThan(c_Finite__Set_Ocard(X1,X2),tc_nat),X1,tc_nat,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_37,plain,
$false,
inference(spm,[status(thm)],[c_0_35,c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT071-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:54:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.85/3.46 % Version : CSE_E---1.7
% 4.85/3.46 % Problem : theBenchmark.p
% 4.85/3.46 % SZS status Unsatisfiable for theBenchmark.p
% 4.85/3.46 % SZS output start CNFRefutation
% See solution above
% 4.85/3.48 % Total time : 2.430s
%------------------------------------------------------------------------------