%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT024-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:28:23 AM UTC 2026
% Result : Unsatisfiable 13.85s 2.53s
% Output : CNFRefutation 13.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 49 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 27 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 20 ( 4 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_irrefl__def_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Relation_Oirrefl(VAR_2,VAR_1)
| ~ hBOOL(c_in(c_Pair(VAR_0,VAR_0,VAR_1,VAR_1),VAR_2,tc_prod(VAR_1,VAR_1))) ),
file('theBenchmark.p',cls_irrefl__def_0) ).
cnf(c_704,plain,
( ~ c_Relation_Oirrefl(C,B)
| ~ hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) ),
inference(clausify,[status(thm)],[cls_irrefl__def_0]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_Relation_Otrans(hAPP(v_P,VAR_0),tc_Arrow__Order__Mirabelle_Oalt),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_711,plain,
c_Relation_Otrans(hAPP(v_P,A),tc_Arrow__Order__Mirabelle_Oalt),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_Relation_Oirrefl(hAPP(v_P,VAR_0),tc_Arrow__Order__Mirabelle_Oalt),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_712,plain,
c_Relation_Oirrefl(hAPP(v_P,A),tc_Arrow__Order__Mirabelle_Oalt),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,VAR_0),tc_Arrow__Order__Mirabelle_Oalt),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_713,plain,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,A),tc_Arrow__Order__Mirabelle_Oalt),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_714,plain,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_715,plain,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_8,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Relation_Otrans(hAPP(VAR_2,v_Pa(VAR_2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(VAR_2,v_Pa(VAR_2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(VAR_2,v_Pa(VAR_2)),tc_Arrow__Order__Mirabelle_Oalt)
| VAR_0 = VAR_1
| ~ hBOOL(c_in(c_Pair(VAR_0,VAR_1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(VAR_2,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(VAR_0,VAR_1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(VAR_2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('theBenchmark.p',cls_conjecture_8) ).
cnf(c_719,plain,
( ~ c_Relation_Otrans(hAPP(C,v_Pa(C)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(C,v_Pa(C)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(C,v_Pa(C)),tc_Arrow__Order__Mirabelle_Oalt)
| A = B
| ~ hBOOL(c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(C,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(C),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(clausify,[status(thm)],[cls_conjecture_8]) ).
cnf(c_4237,plain,
~ hBOOL(c_in(c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,B),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(resolve,[status(thm)],[c_712,c_704]) ).
cnf(c_4399,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a = v_b
| hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolve,[status(thm)],[c_719,c_714]) ).
cnf(c_4400,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b = v_a
| hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(copy,[status(thm)],[c_4399]) ).
cnf(c_4401,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b = v_a ),
inference(resolve,[status(thm)],[c_715,c_4400]) ).
cnf(c_4402,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b = v_a ),
inference(resolve,[status(thm)],[c_713,c_4401]) ).
cnf(c_4403,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b = v_a ),
inference(resolve,[status(thm)],[c_712,c_4402]) ).
cnf(c_4334,plain,
v_b = v_a,
inference(resolve,[status(thm)],[c_711,c_4403]) ).
cnf(c_4404,plain,
hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(paramod,[status(thm)],[c_4334,c_714]) ).
cnf(c_4398,plain,
$false,
inference(resolve,[status(thm)],[c_4237,c_4404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT024-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n004.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sat Sep 26 06:19:39 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 992551 was started by sandbox2 on n004,
% 0.17/0.45 % Sat Sep 26 06:19:39 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.50
% 0.17/0.50 % From the command line: assign(max_seconds, 300).
% 13.85/2.53
% 13.85/2.53 % given #500 (I,wt=51): 703 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(c_Pair(E,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(c_Pair(A,E,C,C),D,tc_prod(C,C))) | -c_Relation_Otrans(D,C) # tptp_name(cls_trans__def_0) # clausal_fof(1). [assumption].
% 13.85/2.53
% 13.85/2.53 % SZS status Unsatisfiable for theBenchmark
% 13.85/2.53
% 13.85/2.53 % Proof 1 at 1.66 (+ 0.26) seconds.
% 13.85/2.53 % Length of proof is 10.
% 13.85/2.53 % Level of proof is 2.
% 13.85/2.53 % Maximum clause weight is 65.000.
% 13.85/2.53 % Given clauses 516.
% 13.85/2.53
% 13.85/2.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------