%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT075-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:28:27 AM UTC 2026
% Result : Unsatisfiable 8.94s 11.66s
% Output : CNFRefutation 8.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 26 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 11 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_complete__Lin_1,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),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(VAR_0,VAR_1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_complete__Lin_1) ).
cnf(c_489,plain,
( A = B
| c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(A,B),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(clausify,[status(thm)],[cls_complete__Lin_1]) ).
fof(cls_complete__Lin_0,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(VAR_0,VAR_1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('theBenchmark.p',cls_complete__Lin_0) ).
cnf(c_490,plain,
( A = B
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(A,B),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(clausify,[status(thm)],[cls_complete__Lin_0]) ).
fof(cls_that_0,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),VAR_0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(VAR_0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_thesis____ ),
file('theBenchmark.p',cls_that_0) ).
cnf(c_552,plain,
( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),A,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(A,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_thesis____ ),
inference(clausify,[status(thm)],[cls_that_0]) ).
fof(cls_CHAINED_0,axiom,
v_a____ != v_b____,
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_554,plain,
v_a____ != v_b____,
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_555,plain,
v_b____ != v_a____,
inference(copy,[status(thm)],[c_554]) ).
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_556,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_646,plain,
( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),A,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(A,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(resolve,[status(thm)],[c_556,c_552]) ).
cnf(c_5274,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(resolve,[status(thm)],[c_555,c_490]) ).
cnf(c_5723,plain,
( v_b____ = v_a____
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(resolve,[status(thm)],[c_646,c_489]) ).
cnf(c_5724,plain,
v_b____ = v_a____,
inference(resolve,[status(thm)],[c_5274,c_5723]) ).
cnf(c_5722,plain,
$false,
inference(resolve,[status(thm)],[c_555,c_5724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT075-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.45 % Computer : n017.cluster.edu
% 0.16/10.45 % Model : x86_64 x86_64
% 0.16/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.45 % Memory : 8046.5625MB
% 0.16/10.45 % OS : Linux 6.8.0-71-generic
% 0.16/10.45 % CPULimit : 300
% 0.16/10.45 % WCLimit : 300
% 0.16/10.45 % DateTime : Sat Sep 26 06:20:30 UTC 2026
% 0.16/10.46 % CPUTime :
% 0.16/10.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/10.46 % Process 43952 was started by sandbox on n017,
% 0.16/10.46 % Sat Sep 26 06:20:30 2026
% 0.16/10.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.21/10.50
% 0.21/10.50 % From the command line: assign(max_seconds, 300).
% 8.94/11.66
% 8.94/11.66 % given #500 (I,wt=56): 609 -c_in(A,B,C) | -c_in(D,B,C) | -c_in(B,c_Equiv__Relations_Oquotient(c_Relation_ODomain(E,C,C),E,C),tc_fun(C,tc_bool)) | c_in(c_Pair(D,A,C,C),E,tc_prod(C,C)) | c_Relation_Orel__comp(c_Relation_Oconverse(E,C,C),E,C,C,C) != E. [copy(608),merge(d)].
% 8.94/11.66
% 8.94/11.66 % SZS status Unsatisfiable for theBenchmark
% 8.94/11.66
% 8.94/11.66 % Proof 1 at 1.00 (+ 0.12) seconds.
% 8.94/11.66 % Length of proof is 9.
% 8.94/11.66 % Level of proof is 3.
% 8.94/11.66 % Maximum clause weight is 34.000.
% 8.94/11.66 % Given clauses 537.
% 8.94/11.66
% 8.94/11.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------