%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET825-1 : 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 08:37:02 AM UTC 2026
% Result : Unsatisfiable 42.06s 7.07s
% Output : CNFRefutation 42.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 48 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 14 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_3,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),VAR_0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(VAR_0)),c_Suc(v_xa(VAR_0)),tc_nat,tc_nat),VAR_0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),VAR_0,tc_prod(tc_nat,tc_nat)) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_1685,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(A)),c_Suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),VAR_0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(VAR_0),v_xa(VAR_0),tc_nat,tc_nat),VAR_0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),VAR_0,tc_prod(tc_nat,tc_nat)) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1686,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
~ v_Q(v_m),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1687,plain,
~ v_Q(v_m),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
v_Q(v_n),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1688,plain,
v_Q(v_n),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Relation_Opair__in__Id__conv__iff1_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ c_in(c_Pair(VAR_0,VAR_1,VAR_2,VAR_2),c_Relation_OId,tc_prod(VAR_2,VAR_2)) ),
file('theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
cnf(c_2010,plain,
( A = B
| ~ c_in(c_Pair(A,B,C,C),c_Relation_OId,tc_prod(C,C)) ),
inference(clausify,[status(thm)],[cls_Relation_Opair__in__Id__conv__iff1_0]) ).
fof(cls_Relation_OIdI_0,axiom,
! [VAR_0,VAR_1] : c_in(c_Pair(VAR_0,VAR_0,VAR_1,VAR_1),c_Relation_OId,tc_prod(VAR_1,VAR_1)),
file('theBenchmark.p',cls_Relation_OIdI_0) ).
cnf(c_2015,plain,
c_in(c_Pair(A,A,B,B),c_Relation_OId,tc_prod(B,B)),
inference(clausify,[status(thm)],[cls_Relation_OIdI_0]) ).
cnf(c_3050,plain,
( c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolve,[status(thm)],[c_2015,c_1686]) ).
cnf(c_20114,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolve,[status(thm)],[c_3050,c_2010]) ).
cnf(c_20103,plain,
( v_xa(c_Relation_OId) = v_x(c_Relation_OId)
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(copy,[status(thm)],[c_20114]) ).
cnf(c_20115,plain,
( v_n = v_m
| v_xa(c_Relation_OId) = v_x(c_Relation_OId) ),
inference(resolve,[status(thm)],[c_20103,c_2010]) ).
cnf(c_20105,plain,
( v_m = v_n
| v_xa(c_Relation_OId) = v_x(c_Relation_OId) ),
inference(copy,[status(thm)],[c_20115]) ).
cnf(c_20116,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_m = v_n ),
inference(paramod,[status(thm)],[c_20105,c_1685]) ).
cnf(c_20117,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_m = v_n ),
inference(resolve,[status(thm)],[c_2015,c_20116]) ).
cnf(c_20109,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_m = v_n ),
inference(resolve,[status(thm)],[c_2015,c_20117]) ).
cnf(c_20118,plain,
( v_n = v_m
| v_m = v_n ),
inference(resolve,[status(thm)],[c_20109,c_2010]) ).
cnf(c_20119,plain,
( v_m = v_n
| v_m = v_n ),
inference(copy,[status(thm)],[c_20118]) ).
cnf(c_20112,plain,
v_m = v_n,
inference(copy,[status(thm)],[c_20119]) ).
cnf(c_20120,plain,
~ v_Q(v_n),
inference(paramod,[status(thm)],[c_20112,c_1687]) ).
cnf(c_20113,plain,
$false,
inference(resolve,[status(thm)],[c_1688,c_20120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:19:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1067392 was started by sandbox on n020,
% 0.10/0.37 % Sat Sep 26 08:19:50 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 42.06/7.07
% 42.06/7.07 % given #500 (I,wt=27): 1834 -c_in(A,B,C) | c_in(c_Sum__Type_OInr(A,C,D),c_Sum__Type_OPlus(E,B,D,C),tc_sum(D,C)) # tptp_name(cls_Sum__Type_OInrI_0) # clausal_fof(1). [assumption].
% 42.06/7.07
% 42.06/7.07 % given #1000 (T,wt=15): 5268 c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat). [resolve(3532,a,5057,a)].
% 42.06/7.07
% 42.06/7.07 % given #1500 (A,wt=33): 2468 -c_lessequals(c_Finite__Set_OFinites,A,tc_set(tc_set(tc_nat))) | c_in(c_SetInterval_OatMost(B,tc_nat),A,tc_set(tc_nat)). [resolve(1857,a,1839,a)].
% 42.06/7.07
% 42.06/7.07 % given #2000 (A,wt=26): 2631 c_in(c_inter(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)). [resolve(1921,a,1861,a)].
% 42.06/7.07
% 42.06/7.07 % given #2500 (A,wt=36): 2783 -c_in(c_Finite__Set_OFinites,A,tc_set(tc_set(tc_nat))) | c_in(c_SetInterval_OatMost(B,tc_nat),c_Union(A,tc_set(tc_nat)),tc_set(tc_nat)). [resolve(1986,a,1857,a)].
% 42.06/7.07
% 42.06/7.07 % given #3000 (A,wt=48): 2928 c_in(c_Pair(A,A,B,B),C,tc_prod(B,B)) | c_in(c_Pair(A,A,B,B),c_minus(c_Transitive__Closure_Ortrancl(D,B),C,tc_set(tc_prod(B,B))),tc_prod(B,B)). [resolve(2002,a,1825,a)].
% 42.06/7.07
% 42.06/7.07 % SZS status Unsatisfiable for theBenchmark
% 42.06/7.07
% 42.06/7.07 % Proof 1 at 4.96 (+ 1.01) seconds.
% 42.06/7.07 % Length of proof is 12.
% 42.06/7.07 % Level of proof is 6.
% 42.06/7.07 % Maximum clause weight is 54.000.
% 42.06/7.07 % Given clauses 3332.
% 42.06/7.07
% 42.06/7.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------