%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET821-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Sun Sep 27 08:37:01 AM UTC 2026
% Result : Unsatisfiable 52.12s 8.07s
% Output : CNFRefutation 52.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 45 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 13 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 32 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_IntDef__Oint_31,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('theBenchmark.p',clsarity_IntDef__Oint_31) ).
cnf(c_1,plain,
class_Orderings_Oorder(tc_IntDef_Oint),
inference(clausify,[status(thm)],[clsarity_IntDef__Oint_31]) ).
fof(cls_Orderings_Oorder__less__irrefl__iff1_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_less(VAR_1,VAR_1,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
cnf(c_7,plain,
( ~ c_less(B,B,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__less__irrefl__iff1_0]) ).
cnf(c_1030,plain,
~ c_less(A,A,tc_IntDef_Oint),
inference(resolve,[status(thm)],[c_1,c_7]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( c_in(v_a,VAR_0,tc_IntDef_Oint)
| ~ c_in(v_b,VAR_0,tc_IntDef_Oint)
| c_in(v_c,VAR_0,tc_IntDef_Oint) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1036,plain,
( c_in(v_a,A,tc_IntDef_Oint)
| ~ c_in(v_b,A,tc_IntDef_Oint)
| c_in(v_c,A,tc_IntDef_Oint) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_less(v_b,v_c,tc_IntDef_Oint),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1037,plain,
c_less(v_b,v_c,tc_IntDef_Oint),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_less(v_a,v_b,tc_IntDef_Oint),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1038,plain,
c_less(v_a,v_b,tc_IntDef_Oint),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Set_OsingletonD__dest_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ c_in(VAR_0,c_insert(VAR_1,c_emptyset,VAR_2),VAR_2) ),
file('theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
cnf(c_1529,plain,
( A = B
| ~ c_in(A,c_insert(B,c_emptyset,C),C) ),
inference(clausify,[status(thm)],[cls_Set_OsingletonD__dest_0]) ).
fof(cls_Set_OinsertE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_1
| c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_insert(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(c_1669,plain,
( A = B
| c_in(A,C,D)
| ~ c_in(A,c_insert(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OinsertE_0]) ).
fof(cls_Set_OinsertCI_1,axiom,
! [VAR_0,VAR_1,VAR_2] : c_in(VAR_0,c_insert(VAR_0,VAR_1,VAR_2),VAR_2),
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(c_1670,plain,
c_in(A,c_insert(A,B,C),C),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_1]) ).
fof(cls_Set_OemptyE_0,axiom,
! [VAR_0,VAR_1] : ~ c_in(VAR_0,c_emptyset,VAR_1),
file('theBenchmark.p',cls_Set_OemptyE_0) ).
cnf(c_1672,plain,
~ c_in(A,c_emptyset,B),
inference(clausify,[status(thm)],[cls_Set_OemptyE_0]) ).
cnf(c_2454,plain,
( c_in(v_a,c_insert(v_b,A,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_c,c_insert(v_b,A,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolve,[status(thm)],[c_1670,c_1036]) ).
cnf(c_20134,plain,
( v_c = v_b
| c_in(v_a,c_insert(v_b,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolve,[status(thm)],[c_2454,c_1529]) ).
cnf(c_20162,plain,
( v_a = v_b
| c_in(v_a,c_emptyset,tc_IntDef_Oint)
| v_c = v_b ),
inference(resolve,[status(thm)],[c_20134,c_1669]) ).
cnf(c_20157,plain,
( v_a = v_b
| v_c = v_b ),
inference(resolve,[status(thm)],[c_1672,c_20162]) ).
cnf(c_20163,plain,
( c_less(v_b,v_b,tc_IntDef_Oint)
| v_a = v_b ),
inference(paramod,[status(thm)],[c_20157,c_1037]) ).
cnf(c_20160,plain,
v_a = v_b,
inference(resolve,[status(thm)],[c_1030,c_20163]) ).
cnf(c_20164,plain,
c_less(v_b,v_b,tc_IntDef_Oint),
inference(paramod,[status(thm)],[c_20160,c_1038]) ).
cnf(c_20161,plain,
$false,
inference(resolve,[status(thm)],[c_1030,c_20164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET821-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.45 % Computer : n004.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Sat Sep 26 08:18:23 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 1218591 was started by sandbox2 on n004,
% 0.16/0.45 % Sat Sep 26 08:18:23 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.50
% 0.22/0.50 % From the command line: assign(max_seconds, 300).
% 52.12/8.07
% 52.12/8.07 % given #500 (I,wt=34): 1019 -c_lessequals(c_SetInterval_OatLeast(A,tc_set(B)),c_SetInterval_OatLeast(C,tc_set(B)),tc_set(tc_set(B))) | c_lessequals(C,A,tc_set(B)). [resolve(9,a,6,a)].
% 52.12/8.07
% 52.12/8.07 % given #1000 (I,wt=27): 1522 -c_in(A,B,C) | c_in(c_Sum__Type_OInl(A,C,D),c_Sum__Type_OPlus(B,E,C,D),tc_sum(C,D)) # tptp_name(cls_Sum__Type_OInlI_0) # clausal_fof(1). [assumption].
% 52.12/8.07
% 52.12/8.07 % given #1500 (W,wt=18): 3841 c_lessequals(A,c_Relation_ODomain(c_UNIV,B,C),tc_set(B)). [resolve(2261,a,1524,a)].
% 52.12/8.07
% 52.12/8.07 % given #2000 (T,wt=20): 3505 class_Finite__Set_Ofinite(tc_sum(tc_Product__Type_Ounit,tc_Datatype_Ooption(tc_Product__Type_Ounit))). [resolve(1972,b,1974,a)].
% 52.12/8.07
% 52.12/8.07 % given #2500 (A,wt=47): 2253 -c_in(c_Pair(c_Pair(A,A,B,B),C,tc_prod(B,B),D),E,tc_prod(tc_prod(B,B),D)) | c_in(C,c_Relation_OImage(E,c_Transitive__Closure_Ortrancl(F,B),tc_prod(B,B),D),D). [resolve(1563,a,1512,a)].
% 52.12/8.07
% 52.12/8.07 % given #3000 (T,wt=22): 13900 -c_lessequals(c_Main_OUnionE__1(c_0,c_Finite__Set_OFinites,tc_nat),A,tc_set(tc_nat)) | c_in(c_0,A,tc_nat). [resolve(13872,a,1526,a)].
% 52.12/8.07
% 52.12/8.07 % SZS status Unsatisfiable for theBenchmark
% 52.12/8.07
% 52.12/8.07 % Proof 1 at 5.94 (+ 1.18) seconds.
% 52.12/8.07 % Length of proof is 15.
% 52.12/8.07 % Level of proof is 5.
% 52.12/8.07 % Maximum clause weight is 24.000.
% 52.12/8.07 % Given clauses 3262.
% 52.12/8.07
% 52.12/8.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------