%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT071-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 : Fri Sep 25 02:40:42 PM UTC 2026
% Result : Unsatisfiable 31.39s 5.34s
% Output : CNFRefutation 31.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 50 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 29 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-5 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f640,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Obij__betw(X0,X1,X4,X2,X3)
| c_Set_Oimage(X0,X1,X2,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_1) ).
fof(f848,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Fun_Obij__betw(X0,X1,X4,X2,X3)
| c_Fun_Oinj__on(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).
fof(f849,axiom,
! [X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(X0,X1),X0,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X0,X1),tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__bij__betw__finite__nat_0) ).
fof(f867,axiom,
c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__indi_0) ).
fof(f907,axiom,
! [X0] : c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_SetInterval_Oord__class_OlessThan(X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast0LessThan_0) ).
fof(f908,plain,
! [X0] : c_SetInterval_Oord__class_OlessThan(X0,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),
inference(reorient_equations,[],[f907]) ).
fof(f924,axiom,
! [X0] :
( v_thesis____
| ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| c_Set_Oimage(X0,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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
fof(f928,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_1353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Set_Oimage(X0,X1,X3,X4) = X2 )
| ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f640]) ).
tcf(c_1527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Fun_Oinj__on(X0,X1,X3,X4)
| ~ c_Fun_Obij__betw(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f848]) ).
tcf(c_1528,plain,
! [X0: $i,X1: $i] :
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(X0,X1),X0,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X0,X1),tc_nat),X1,tc_nat)
| ~ c_Finite__Set_Ofinite(X0,X1) ),
inference(cnf_transformation,[],[f849]) ).
tcf(c_1543,plain,
c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),
inference(cnf_transformation,[],[f867]) ).
tcf(c_1570,plain,
! [X0: $i] : c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_SetInterval_Oord__class_OlessThan(X0,tc_nat),
inference(cnf_transformation,[],[f908]) ).
tcf(c_1583,plain,
! [X0: $i] :
( v_thesis____
| ~ c_Fun_Oinj__on(X0,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_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ) ),
inference(cnf_transformation,[],[f924]) ).
tcf(c_1587,negated_conjecture,
~ v_thesis____,
inference(cnf_transformation,[],[f928]) ).
tcf(c_2414,plain,
! [X0: $i,X1: $i] :
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(X0,X1),X0,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X0,X1),tc_nat),X1,tc_nat)
| ~ c_Finite__Set_Ofinite(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1528]) ).
tcf(c_2756,plain,
! [X0: $i] :
( ~ c_Fun_Oinj__on(X0,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_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ) ),
inference(prop_impl_just,[status(thm)],[c_1587,c_1583]) ).
tcf(c_6759,plain,
! [X0: $i,X1: $i] :
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(X0,X1),X0,c_SetInterval_Oord__class_OlessThan(c_Finite__Set_Ocard(X0,X1),tc_nat),X1,tc_nat)
| ~ c_Finite__Set_Ofinite(X0,X1) ),
inference(demodulation,[status(thm)],[c_2414,c_1570]) ).
tcf(c_6774,plain,
! [X0: $i] :
( ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(X0,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) ) ),
inference(demodulation,[status(thm)],[c_2756,c_1570]) ).
tcf(c_8624,plain,
! [X0: $i,X1: $i] :
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(X0,X1),X0,c_SetInterval_Oord__class_OlessThan(c_Finite__Set_Ocard(X0,X1),tc_nat),X1,tc_nat)
| ~ c_Finite__Set_Ofinite(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_6759]) ).
tcf(c_8960,plain,
! [X0: $i] :
( ( c_Set_Oimage(X0,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(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(prop_impl_just,[status(thm)],[c_6774]) ).
tcf(c_8961,plain,
! [X0: $i] :
( ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ( c_Set_Oimage(X0,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) ) ),
inference(renaming,[status(thm)],[c_8960]) ).
tcf(c_19012,plain,
! [X0: $i,X1: $i] :
( c_Fun_Oinj__on(X0,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(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),X1,tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(instantiation,[status(thm)],[c_1527]) ).
tcf(c_20837,plain,
( c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),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_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),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),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(instantiation,[status(thm)],[c_19012]) ).
tcf(c_21755,plain,
( c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),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),tc_Arrow__Order__Mirabelle_Oindi,tc_nat)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi) ),
inference(instantiation,[status(thm)],[c_8624]) ).
tcf(c_24112,plain,
( ~ c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),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_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),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) ) ),
inference(instantiation,[status(thm)],[c_8961]) ).
tcf(c_27892,plain,
( ( c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),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(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),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),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ),
inference(instantiation,[status(thm)],[c_1353]) ).
tcf(c_27893,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_27892,c_24112,c_21755,c_20837,c_1543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT071-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 08:36:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 31.39/5.34 % SZS status Started for theBenchmark.p
% 31.39/5.34 % SZS status Unsatisfiable for theBenchmark.p
% 31.39/5.34
% 31.39/5.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.39/5.34
% 31.39/5.34 % ------ iProver source info
% 31.39/5.34
% 31.39/5.34 % git: date: 2026-07-19 20:42:38 +0200
% 31.39/5.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.39/5.34 % git: non_committed_changes: false
% 31.39/5.34
% 31.39/5.34 % ------ Parsing...% successful
% 31.39/5.34
% 31.39/5.34
% 31.39/5.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.39/5.34
% 31.39/5.34 % ------ Preprocessing... sup_sim: 30 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 1 sf_s rm: 11 0s sf_e pe_s pe_e %
% 31.39/5.34
% 31.39/5.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.39/5.34
% 31.39/5.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e
% 31.39/5.34 % ------ Proving...
% 31.39/5.34 % ------ Problem Properties
% 31.39/5.34
% 31.39/5.34 %
% 31.39/5.34 % clauses 596
% 31.39/5.34 % conjectures 0
% 31.39/5.34 % EPR 55
% 31.39/5.34 % Horn 543
% 31.39/5.34 % unary 159
% 31.39/5.34 % binary 271
% 31.39/5.34 % lits 1243
% 31.39/5.34 % lits eq 350
% 31.39/5.34 % fd_pure 0
% 31.39/5.34 % fd_pseudo 0
% 31.39/5.34 % fd_cond 5
% 31.39/5.34 % fd_pseudo_cond 47
% 31.39/5.34 % AC symbols 0
% 31.39/5.34
% 31.39/5.34 % ------ Input Options Time Limit: Unbounded
% 31.39/5.34
% 31.39/5.34
% 31.39/5.34 % ------
% 31.39/5.34 % Current options:
% 31.39/5.34 % ------
% 31.39/5.34
% 31.39/5.34
% 31.39/5.34 %
% 31.39/5.34
% 31.39/5.34 % ------ Proving...
% 31.39/5.34 %
% 31.39/5.34
% 31.39/5.34 % SZS status Unsatisfiable for theBenchmark.p
% 31.39/5.34
% 31.39/5.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.39/5.34
% 31.39/5.34
%------------------------------------------------------------------------------