%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET820-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 116.02s 21.28s
% Output : CNFRefutation 116.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 21 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 6 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1056,plain,
c_in(A,c_insert(A,B,C),C),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_1]) ).
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_1198,plain,
( A = B
| ~ c_in(A,c_insert(B,c_emptyset,C),C) ),
inference(clausify,[status(thm)],[cls_Set_OsingletonD__dest_0]) ).
fof(cls_conjecture_0,axiom,
v_P(v_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1547,plain,
v_P(v_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0,VAR_1] :
( c_in(v_x(VAR_1),VAR_1,tc_IntDef_Oint)
| ~ c_in(VAR_0,VAR_1,tc_IntDef_Oint) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1548,plain,
( c_in(v_x(B),B,tc_IntDef_Oint)
| ~ c_in(A,B,tc_IntDef_Oint) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0,VAR_1] :
( ~ v_P(v_x(VAR_1))
| ~ c_in(VAR_0,VAR_1,tc_IntDef_Oint) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1549,plain,
( ~ v_P(v_x(B))
| ~ c_in(A,B,tc_IntDef_Oint) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_2707,plain,
c_in(v_x(c_insert(A,B,tc_IntDef_Oint)),c_insert(A,B,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolve,[status(thm)],[c_1548,c_1056]) ).
cnf(c_2712,plain,
~ v_P(v_x(c_insert(A,B,tc_IntDef_Oint))),
inference(resolve,[status(thm)],[c_1549,c_1056]) ).
cnf(c_18961,plain,
v_x(c_insert(A,c_emptyset,tc_IntDef_Oint)) = A,
inference(resolve,[status(thm)],[c_2707,c_1198]) ).
cnf(c_18965,plain,
~ v_P(A),
inference(paramod,[status(thm)],[c_18961,c_2712]) ).
cnf(c_18966,plain,
$false,
inference(resolve,[status(thm)],[c_18965,c_1547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET820-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.41 % Computer : n001.cluster.edu
% 0.12/5.41 % Model : x86_64 x86_64
% 0.12/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.41 % Memory : 8046.5625MB
% 0.12/5.41 % OS : Linux 6.8.0-71-generic
% 0.12/5.41 % CPULimit : 300
% 0.12/5.41 % WCLimit : 300
% 0.12/5.41 % DateTime : Sat Sep 26 08:24:19 UTC 2026
% 0.12/5.41 % CPUTime :
% 0.12/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.41 % Process 1360886 was started by sandbox on n001,
% 0.12/5.41 % Sat Sep 26 08:24:19 2026
% 0.12/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/5.46
% 0.12/5.46 % From the command line: assign(max_seconds, 300).
% 116.02/21.28
% 116.02/21.28 % given #500 (I,wt=9): 1504 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # tptp_name(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) # clausal_fof(1). [assumption].
% 116.02/21.28
% 116.02/21.28 % given #1000 (I,wt=25): 2027 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(62,a,48,b)].
% 116.02/21.28
% 116.02/21.28 % given #1500 (W,wt=21): 3765 -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),B,tc_set(tc_IntDef_Oint)) | c_in(A,B,tc_IntDef_Oint). [resolve(2772,a,1200,a)].
% 116.02/21.28
% 116.02/21.28 % given #2000 (W,wt=23): 3683 class_Finite__Set_Ofinite(tc_sum(tc_Product__Type_Ounit,tc_sum(tc_bool,tc_bool))). [resolve(2704,b,3103,a)].
% 116.02/21.28
% 116.02/21.28 % given #2500 (W,wt=25): 2338 c_in(c_inter(c_SetInterval_OatMost(A,tc_nat),B,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)). [resolve(1183,a,1117,a)].
% 116.02/21.28
% 116.02/21.28 % given #3000 (W,wt=25): 18594 c_union(A,c_SetInterval_OatLeast(c_0,tc_nat),B) = c_SetInterval_OatLeast(c_0,tc_nat). [resolve(18593,a,5095,a),flip(a)].
% 116.02/21.28
% 116.02/21.28 % SZS status Unsatisfiable for theBenchmark
% 116.02/21.28
% 116.02/21.28 % Proof 1 at 6.04 (+ 1.49) seconds.
% 116.02/21.28 % Length of proof is 10.
% 116.02/21.28 % Level of proof is 4.
% 116.02/21.28 % Maximum clause weight is 26.000.
% 116.02/21.28 % Given clauses 3105.
% 116.02/21.28
% 116.02/21.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------