%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 0.16s 5.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 72 ( 39 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 52 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_Comb_Odiamond(v_r,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_Comb_Odiamond(v_r,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Comb_Odiamond__strip__lemmaE_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(c_Pair(VAR_4,c_Comb_Odiamond__strip__lemmaE__1(VAR_0,VAR_4,VAR_3,VAR_1),VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_in(c_Pair(VAR_2,VAR_4,VAR_1,VAR_1),c_Transitive__Closure_Ortrancl(VAR_0,VAR_1),tc_prod(VAR_1,VAR_1))
| ~ c_in(c_Pair(VAR_2,VAR_3,VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_Comb_Odiamond(VAR_0,VAR_1) ),
file('theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
cnf(c_2,plain,
( c_in(c_Pair(E,c_Comb_Odiamond__strip__lemmaE__1(A,E,D,B),B,B),A,tc_prod(B,B))
| ~ c_in(c_Pair(C,E,B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B))
| ~ c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_Comb_Odiamond(A,B) ),
inference(clausify,[status(thm)],[cls_Comb_Odiamond__strip__lemmaE_1]) ).
fof(cls_Comb_Odiamond__strip__lemmaE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(c_Pair(VAR_3,c_Comb_Odiamond__strip__lemmaE__1(VAR_0,VAR_4,VAR_3,VAR_1),VAR_1,VAR_1),c_Transitive__Closure_Ortrancl(VAR_0,VAR_1),tc_prod(VAR_1,VAR_1))
| ~ c_in(c_Pair(VAR_2,VAR_4,VAR_1,VAR_1),c_Transitive__Closure_Ortrancl(VAR_0,VAR_1),tc_prod(VAR_1,VAR_1))
| ~ c_in(c_Pair(VAR_2,VAR_3,VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_Comb_Odiamond(VAR_0,VAR_1) ),
file('theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_0) ).
cnf(c_3,plain,
( c_in(c_Pair(D,c_Comb_Odiamond__strip__lemmaE__1(A,E,D,B),B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B))
| ~ c_in(c_Pair(C,E,B,B),c_Transitive__Closure_Ortrancl(A,B),tc_prod(B,B))
| ~ c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_Comb_Odiamond(A,B) ),
inference(clausify,[status(thm)],[cls_Comb_Odiamond__strip__lemmaE_0]) ).
cnf(c_4,plain,
( c_in(c_Pair(B,c_Comb_Odiamond__strip__lemmaE__1(v_r,C,B,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,C,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_5,plain,
( c_in(c_Pair(C,c_Comb_Odiamond__strip__lemmaE__1(v_r,C,B,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,C,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,B,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_conjecture_6,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_z,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_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_6) ).
cnf(c_6,plain,
( ~ c_in(c_Pair(v_z,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ 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)) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_y,VAR_0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(VAR_0,v_x(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_5) ).
cnf(c_7,plain,
( ~ c_in(c_Pair(v_y,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_x(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_5]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_y,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_ya,v_x(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_4) ).
cnf(c_8,plain,
( ~ c_in(c_Pair(v_y,A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(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_4]) ).
fof(cls_conjecture_3,axiom,
c_in(c_Pair(v_y,v_xaa,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_9,plain,
c_in(c_Pair(v_y,v_xaa,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_2,axiom,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_10,plain,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
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_11,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_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_12,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]) ).
cnf(c_14,plain,
( ~ 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(B,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,A,v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_17,plain,
c_in(c_Pair(v_ya,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_18,plain,
c_in(c_Pair(v_xaa,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_160,plain,
( c_in(c_Pair(A,c_Comb_Odiamond__strip__lemmaE__1(v_r,A,v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,A,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_10]) ).
cnf(c_46,plain,
c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_160,c_17]) ).
cnf(c_161,plain,
( ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_14,c_17]) ).
cnf(c_64,plain,
~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_10,c_161]) ).
cnf(c_162,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(v_xaa),A,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolve,[status(thm)],[c_11,c_18]) ).
cnf(c_108,plain,
~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_162,c_64]) ).
cnf(c_163,plain,
c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_12,c_46]) ).
cnf(c_159,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n016.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 23:22:21 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.44 % Process 1996426 was started by sandbox2 on n016,
% 0.16/5.44 % Sat Sep 26 23:22:21 2026
% 0.16/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.45
% 0.16/5.45 % From the command line: assign(max_seconds, 300).
% 0.16/5.48
% 0.16/5.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.48
% 0.16/5.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.16/5.48 % Length of proof is 19.
% 0.16/5.48 % Level of proof is 5.
% 0.16/5.48 % Maximum clause weight is 38.000.
% 0.16/5.48 % Given clauses 51.
% 0.16/5.48
% 0.16/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------