%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL123-2 : 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 : n020.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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 30 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 39 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Transitive__Closure_Or__into__rtrancl_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Transitive__Closure_Ortrancl(VAR_1,VAR_2),tc_prod(VAR_2,VAR_2))
| ~ c_in(VAR_0,VAR_1,tc_prod(VAR_2,VAR_2)) ),
file('theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
cnf(c_1,plain,
( c_in(A,c_Transitive__Closure_Ortrancl(B,C),tc_prod(C,C))
| ~ c_in(A,B,tc_prod(C,C)) ),
inference(clausify,[status(thm)],[cls_Transitive__Closure_Or__into__rtrancl_0]) ).
fof(cls_Transitive__Closure_Ortrancl__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(c_Pair(VAR_4,VAR_1,VAR_2,VAR_2),c_Transitive__Closure_Ortrancl(VAR_3,VAR_2),tc_prod(VAR_2,VAR_2))
| ~ c_in(c_Pair(VAR_4,VAR_0,VAR_2,VAR_2),c_Transitive__Closure_Ortrancl(VAR_3,VAR_2),tc_prod(VAR_2,VAR_2))
| ~ c_in(c_Pair(VAR_0,VAR_1,VAR_2,VAR_2),c_Transitive__Closure_Ortrancl(VAR_3,VAR_2),tc_prod(VAR_2,VAR_2)) ),
file('theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
cnf(c_2,plain,
( c_in(c_Pair(E,B,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C))
| ~ c_in(c_Pair(E,A,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C))
| ~ c_in(c_Pair(A,B,C,C),c_Transitive__Closure_Ortrancl(D,C),tc_prod(C,C)) ),
inference(clausify,[status(thm)],[cls_Transitive__Closure_Ortrancl__trans_0]) ).
fof(cls_conjecture_1,axiom,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_3,plain,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_4,plain,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_x,VAR_0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(VAR_0,v_xaa(VAR_0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_5,plain,
( ~ c_in(c_Pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(A,v_xaa(A),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_x,VAR_0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_xaa(VAR_0),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_6,plain,
( ~ c_in(c_Pair(v_x,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_xaa(A),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_xb,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_z,VAR_0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_7,plain,
( ~ c_in(c_Pair(v_xb,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_in(c_Pair(VAR_1,VAR_0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(VAR_1,VAR_2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(VAR_0,v_xa(VAR_1,VAR_0,VAR_2),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_8,plain,
( ~ c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(A,v_xa(B,A,C),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_7,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_in(c_Pair(VAR_1,VAR_2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(VAR_1,VAR_0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(VAR_0,v_xa(VAR_1,VAR_2,VAR_0),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('theBenchmark.p',cls_conjecture_7) ).
cnf(c_9,plain,
( ~ c_in(c_Pair(B,C,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(A,v_xa(B,C,A),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_7]) ).
cnf(c_12,plain,
c_in(c_Pair(v_xb,v_xaa(v_xb),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_13,plain,
c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_15,plain,
( ~ c_in(c_Pair(v_xb,B,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(B,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_107,plain,
( ~ c_in(c_Pair(v_y,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,A,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_9,c_13]) ).
cnf(c_36,plain,
c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_107,c_3]) ).
cnf(c_108,plain,
( ~ c_in(c_Pair(v_y,A,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(A,v_xa(v_y,A,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_8,c_13]) ).
cnf(c_38,plain,
c_in(c_Pair(v_z,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_108,c_3]) ).
cnf(c_109,plain,
( ~ c_in(c_Pair(v_xb,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_15,c_38]) ).
cnf(c_101,plain,
~ c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_109,c_12]) ).
cnf(c_110,plain,
c_in(c_Pair(v_xaa(v_xb),v_xa(v_y,v_z,v_xaa(v_xb)),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_1,c_36]) ).
cnf(c_106,plain,
$false,
inference(resolve,[status(thm)],[c_101,c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL123-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 23:18:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2775876 was started by sandbox on n020,
% 0.08/0.36 % Sat Sep 26 23:18:04 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 16.
% 0.08/0.38 % Level of proof is 4.
% 0.08/0.38 % Maximum clause weight is 36.000.
% 0.08/0.38 % Given clauses 36.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------