%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT023-1 : 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 : n005.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 16.64s 3.25s
% Output : CNFRefutation 16.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 57 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 19 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 42 ( 4 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_8,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ c_in(c_Pair(VAR_0,VAR_1,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))
| c_in(c_Pair(VAR_0,VAR_1,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_8) ).
cnf(c_153,plain,
( A = B
| ~ c_in(c_Pair(A,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))
| c_in(c_Pair(A,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_8]) ).
fof(cls_conjecture_6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_0
| c_in(c_Pair(VAR_1,VAR_0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,VAR_2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(VAR_0,VAR_1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,VAR_2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_155,plain,
( B = A
| c_in(c_Pair(B,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,C),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,C),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_5,axiom,
~ 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_5) ).
cnf(c_156,plain,
~ 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_5]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0] : ~ c_in(c_Pair(VAR_0,VAR_0,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_157,plain,
~ c_in(c_Pair(A,A,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_3,axiom,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_158,plain,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
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_2) ).
cnf(c_159,plain,
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_2]) ).
fof(cls_mem__def_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_in(VAR_1,VAR_0,VAR_2)
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(c_162,plain,
( ~ c_in(B,A,C)
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_mem__def_0]) ).
fof(cls_mem__def_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(VAR_1,VAR_0))
| c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(c_163,plain,
( ~ hBOOL(hAPP(B,A))
| c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_mem__def_1]) ).
fof(cls_transD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Relation_Otrans(VAR_3,VAR_2)
| ~ c_in(c_Pair(VAR_0,VAR_4,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2))
| ~ c_in(c_Pair(VAR_4,VAR_1,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2))
| c_in(c_Pair(VAR_0,VAR_1,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2)) ),
file('theBenchmark.p',cls_transD_0) ).
cnf(c_164,plain,
( ~ c_Relation_Otrans(D,C)
| ~ c_in(c_Pair(A,E,C,C),D,tc_prod(C,C))
| ~ c_in(c_Pair(E,B,C,C),D,tc_prod(C,C))
| c_in(c_Pair(A,B,C,C),D,tc_prod(C,C)) ),
inference(clausify,[status(thm)],[cls_transD_0]) ).
cnf(c_7628,plain,
( B = A
| c_in(c_Pair(B,A,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))
| B = A
| c_in(c_Pair(A,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(resolve,[status(thm)],[c_155,c_153]) ).
cnf(c_780,plain,
( c_in(c_Pair(B,A,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))
| B = A
| c_in(c_Pair(A,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(copy,[status(thm)],[c_7628]) ).
cnf(c_782,plain,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(resolve,[status(thm)],[c_162,c_159]) ).
cnf(c_7629,plain,
( ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(A,v_a,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))
| c_in(c_Pair(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_164,c_159]) ).
cnf(c_787,plain,
( ~ c_in(c_Pair(A,v_a,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))
| c_in(c_Pair(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_158,c_7629]) ).
cnf(c_6552,plain,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),A),
inference(resolve,[status(thm)],[c_782,c_163]) ).
cnf(c_6958,plain,
( c_in(c_Pair(v_b,v_a,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))
| v_b = v_a ),
inference(resolve,[status(thm)],[c_780,c_156]) ).
cnf(c_7630,plain,
( v_b = v_a
| c_in(c_Pair(v_b,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_787,c_6958]) ).
cnf(c_7549,plain,
v_b = v_a,
inference(resolve,[status(thm)],[c_157,c_7630]) ).
cnf(c_7626,plain,
c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),A),
inference(paramod,[status(thm)],[c_7549,c_6552]) ).
cnf(c_7627,plain,
$false,
inference(resolve,[status(thm)],[c_7626,c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT023-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:19:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1405514 was started by sandbox2 on n005,
% 0.09/0.37 % Sat Sep 26 06:19:33 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 16.64/3.25
% 16.64/3.25 % given #500 (I,wt=80): 669 c_in(c_Pair(A,B,C,C),D,tc_prod(C,C)) | -c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)),C) | c_Relation_Orel__comp(c_Relation_Oconverse(D,C,C),D,C,C,C) != D. [resolve(68,c,50,b)].
% 16.64/3.25
% 16.64/3.25 % SZS status Unsatisfiable for theBenchmark
% 16.64/3.25
% 16.64/3.25 % Proof 1 at 2.31 (+ 0.48) seconds.
% 16.64/3.25 % Length of proof is 17.
% 16.64/3.25 % Level of proof is 5.
% 16.64/3.25 % Maximum clause weight is 43.000.
% 16.64/3.25 % Given clauses 784.
% 16.64/3.25
% 16.64/3.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------