%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL122-1 : 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 : n026.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 06:57:47 AM UTC 2026
% Result : Unsatisfiable 25.02s 8.65s
% Output : CNFRefutation 25.02s
% 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 : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 8 ( 1 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_1,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_xaa,VAR_0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,VAR_0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1620,plain,
( ~ c_in(c_Pair(v_xaa,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1621,plain,
c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_in(c_Pair(VAR_0,VAR_0,VAR_1,VAR_1),c_Transitive__Closure_Ortrancl(VAR_2,VAR_1),tc_prod(VAR_1,VAR_1)),
file('theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
cnf(c_1796,plain,
c_in(c_Pair(A,A,B,B),c_Transitive__Closure_Ortrancl(C,B),tc_prod(B,B)),
inference(clausify,[status(thm)],[cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0]) ).
cnf(c_2210,plain,
~ c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_1796,c_1620]) ).
cnf(c_2209,plain,
$false,
inference(resolve,[status(thm)],[c_1621,c_2210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL122-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.40 % Computer : n026.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.40 % DateTime : Sat Sep 26 23:20:17 UTC 2026
% 0.14/5.40 % CPUTime :
% 0.14/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/5.41 % Process 2208600 was started by sandbox on n026,
% 0.14/5.41 % Sat Sep 26 23:20:17 2026
% 0.14/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.46
% 0.14/5.46 % From the command line: assign(max_seconds, 300).
% 25.02/8.65
% 25.02/8.65 % given #500 (I,wt=9): 1646 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__semiring(A) # tptp_name(clsrel_Ring__and__Field_Oordered__semidom_36) # clausal_fof(1). [assumption].
% 25.02/8.65
% 25.02/8.65 % SZS status Unsatisfiable for theBenchmark
% 25.02/8.65
% 25.02/8.65 % Proof 1 at 3.10 (+ 0.05) seconds.
% 25.02/8.65 % Length of proof is 4.
% 25.02/8.65 % Level of proof is 1.
% 25.02/8.65 % Maximum clause weight is 32.000.
% 25.02/8.65 % Given clauses 650.
% 25.02/8.65
% 25.02/8.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------