%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL112-1 : 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 : 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 06:57:45 AM UTC 2026
% Result : Unsatisfiable 20.82s 3.54s
% Output : CNFRefutation 20.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 8 ( 1 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_x,VAR_0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),VAR_0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1069,plain,
( ~ c_in(c_Pair(v_x,A,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),A,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Comb_Oparcontract_Ointros__2_0,axiom,
! [VAR_0,VAR_1] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,VAR_0),VAR_1),VAR_0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('theBenchmark.p',cls_Comb_Oparcontract_Ointros__2_0) ).
cnf(c_1963,plain,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,A),B),A,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(clausify,[status(thm)],[cls_Comb_Oparcontract_Ointros__2_0]) ).
fof(cls_Comb_Oparcontract_Ointros__1_0,axiom,
! [VAR_0] : c_in(c_Pair(VAR_0,VAR_0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('theBenchmark.p',cls_Comb_Oparcontract_Ointros__1_0) ).
cnf(c_1964,plain,
c_in(c_Pair(A,A,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(clausify,[status(thm)],[cls_Comb_Oparcontract_Ointros__1_0]) ).
cnf(c_3708,plain,
~ c_in(c_Pair(v_x,v_x,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolve,[status(thm)],[c_1963,c_1069]) ).
cnf(c_3707,plain,
$false,
inference(resolve,[status(thm)],[c_1964,c_3708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL112-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n004.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Sat Sep 26 23:16:21 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.46 % Process 2872178 was started by sandbox on n004,
% 0.21/0.46 % Sat Sep 26 23:16:21 2026
% 0.21/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.24/0.53
% 0.24/0.53 % From the command line: assign(max_seconds, 300).
% 20.82/3.54
% 20.82/3.54 % given #500 (I,wt=22): 1333 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(87,b,67,a)].
% 20.82/3.54
% 20.82/3.54 % given #1000 (I,wt=36): 1891 -c_in(c_minus(A,B,tc_set(C)),c_Finite__Set_OFinites,tc_set(C)) | c_in(c_minus(A,c_insert(D,B,C),tc_set(C)),c_Finite__Set_OFinites,tc_set(C)) # tptp_name(cls_Finite__Set_Ofinite__Diff__insert__iff2_0) # clausal_fof(1). [assumption].
% 20.82/3.54
% 20.82/3.54 % SZS status Unsatisfiable for theBenchmark
% 20.82/3.54
% 20.82/3.54 % Proof 1 at 2.86 (+ 0.10) seconds.
% 20.82/3.54 % Length of proof is 4.
% 20.82/3.54 % Level of proof is 1.
% 20.82/3.54 % Maximum clause weight is 44.000.
% 20.82/3.54 % Given clauses 1046.
% 20.82/3.54
% 20.82/3.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------