%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL118-1 : 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 : n002.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 06:57:46 AM UTC 2026
% Result : Unsatisfiable 30.14s 4.41s
% Output : CNFRefutation 30.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Comb_Oparcontract_Ointros__4_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(VAR_2,VAR_0),c_Comb_Ocomb_Oop_A_D_D(VAR_3,VAR_1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(VAR_2,VAR_3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(VAR_0,VAR_1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('theBenchmark.p',cls_Comb_Oparcontract_Ointros__4_0) ).
cnf(c_1291,plain,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(C,A),c_Comb_Ocomb_Oop_A_D_D(D,B),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(C,D,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(A,B,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__4_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_1294,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]) ).
fof(cls_conjecture_0,axiom,
c_in(c_Pair(v_x,v_ya,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_1629,plain,
c_in(c_Pair(v_x,v_ya,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_conjecture_1,axiom,
c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1630,plain,
c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),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(v_x,v_z),VAR_0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1631,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),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(v_x,v_z),A,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_3982,plain,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(A,v_z),c_Comb_Ocomb_Oop_A_D_D(B,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(A,B,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(resolve,[status(thm)],[c_1291,c_1630]) ).
cnf(c_3942,plain,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolve,[status(thm)],[c_3982,c_1629]) ).
cnf(c_3983,plain,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolve,[status(thm)],[c_1631,c_1294]) ).
cnf(c_3981,plain,
$false,
inference(resolve,[status(thm)],[c_3942,c_3983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL118-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 23:19:36 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 2932912 was started by sandbox on n002,
% 0.19/0.46 % Sat Sep 26 23:19:36 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.23/0.52
% 0.23/0.52 % From the command line: assign(max_seconds, 300).
% 30.14/4.41
% 30.14/4.41 % given #500 (I,wt=17): 1027 c_Divides_Oop_Advd(A,c_times(A,B,tc_nat),tc_nat) # tptp_name(cls_Divides_Odvd__triv__left_0) # clausal_fof(1). [assumption].
% 30.14/4.41
% 30.14/4.41 % given #1000 (I,wt=9): 1612 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Opordered__semiring(A) # tptp_name(clsrel_Ring__and__Field_Opordered__comm__semiring_15) # clausal_fof(1). [assumption].
% 30.14/4.41
% 30.14/4.41 % SZS status Unsatisfiable for theBenchmark
% 30.14/4.41
% 30.14/4.41 % Proof 1 at 3.56 (+ 0.25) seconds.
% 30.14/4.41 % Length of proof is 7.
% 30.14/4.41 % Level of proof is 2.
% 30.14/4.41 % Maximum clause weight is 49.000.
% 30.14/4.41 % Given clauses 1019.
% 30.14/4.41
% 30.14/4.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------