%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET988+1 : 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 : n026.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 08:37:25 AM UTC 2026
% Result : Theorem 0.82s 0.57s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 119 ( 32 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 138 ( 54 ~; 48 |; 29 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 86 ( 6 sgn 59 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_funct_1,axiom,
! [A] :
( function(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
=> C = D ) ),
file('theBenchmark.p',d1_funct_1) ).
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(t2_funct_1,conjecture,
! [A] :
( ( ! [B,C,D] :
( ( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
=> C = D )
& ! [B] :
~ ( ! [C,D] : ordered_pair(C,D) != B
& in(B,A) ) )
=> ( function(A)
& relation(A) ) ),
file('theBenchmark.p',t2_funct_1) ).
fof(t2_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( ! [B,C,D] :
( ( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
=> C = D )
& ! [B] :
~ ( ! [C,D] : ordered_pair(C,D) != B
& in(B,A) ) )
=> ( function(A)
& relation(A) ) ),
inference(assume_negation,[status(cth)],[t2_funct_1]) ).
fof(nnf_30,plain,
! [A] :
( ( ? [B,C,D] :
( D != C
& in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
| function(A) )
& ( ! [X0,X1,X2] :
( X2 = X1
| ~ in(ordered_pair(X0,X2),A)
| ~ in(ordered_pair(X0,X1),A) )
| ~ function(A) ) ),
inference(fof_nnf,[status(thm)],[d1_funct_1]) ).
fof(sk_d1_funct_1_sk,plain,
! [A] :
( ( ( sK2(A) != sK1(A)
& in(ordered_pair(sK0(A),sK2(A)),A)
& in(ordered_pair(sK0(A),sK1(A)),A) )
| function(A) )
& ( ! [X0,X1,X2] :
( X2 = X1
| ~ in(ordered_pair(X0,X2),A)
| ~ in(ordered_pair(X0,X1),A) )
| ~ function(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B,sK0(A)),skolemize(C,sK1(A)),skolemize(D,sK2(A))],[nnf_30]) ).
fof(sk_d1_funct_1,plain,
( ! [VAR_0] :
( sK2(VAR_0) != sK1(VAR_0)
| function(VAR_0) )
& ! [VAR_0] :
( in(ordered_pair(sK0(VAR_0),sK2(VAR_0)),VAR_0)
| function(VAR_0) )
& ! [VAR_0] :
( in(ordered_pair(sK0(VAR_0),sK1(VAR_0)),VAR_0)
| function(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ in(ordered_pair(VAR_1,VAR_3),VAR_0)
| ~ in(ordered_pair(VAR_1,VAR_2),VAR_0)
| ~ function(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_funct_1_sk]) ).
cnf(c_69,plain,
( in(ordered_pair(sK0(A),sK1(A)),A)
| function(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_funct_1]) ).
cnf(c_70,plain,
( in(ordered_pair(sK0(A),sK2(A)),A)
| function(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_funct_1]) ).
cnf(c_71,plain,
( sK2(A) != sK1(A)
| function(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_funct_1]) ).
fof(nnf_31,plain,
! [A] :
( ( ? [B] :
( ! [C,D] : ordered_pair(C,D) != B
& in(B,A) )
| relation(A) )
& ( ! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
| ~ in(X0,A) )
| ~ relation(A) ) ),
inference(fof_nnf,[status(thm)],[d1_relat_1]) ).
fof(sk_d1_relat_1_sk,plain,
! [A] :
( ( ( ! [C,D] : ordered_pair(C,D) != sK3(A)
& in(sK3(A),A) )
| relation(A) )
& ( ! [X0] :
( ordered_pair(sK7(A,X0),sK8(A,X0)) = X0
| ~ in(X0,A) )
| ~ relation(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK3]),skolemize(X1,sK7(A,X0)),skolemize(X2,sK8(A,X0)),skolemize(B,sK3(A))],[nnf_31]) ).
fof(sk_d1_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ordered_pair(VAR_1,VAR_2) != sK3(VAR_0)
| relation(VAR_0) )
& ! [VAR_0] :
( in(sK3(VAR_0),VAR_0)
| relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( ordered_pair(sK7(VAR_0,VAR_1),sK8(VAR_0,VAR_1)) = VAR_1
| ~ in(VAR_1,VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_relat_1_sk]) ).
cnf(c_73,plain,
( in(sK3(A),A)
| relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_relat_1]) ).
cnf(c_74,plain,
( ordered_pair(B,C) != sK3(A)
| relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_relat_1]) ).
cnf(c_75,plain,
( sK3(A) != ordered_pair(B,C)
| relation(A) ),
inference(copy,[status(thm)],[c_74]) ).
fof(nnf_32,plain,
? [A] :
( ( ~ function(A)
| ~ relation(A) )
& ! [B,C,D] :
( D = C
| ~ in(ordered_pair(B,D),A)
| ~ in(ordered_pair(B,C),A) )
& ! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
| ~ in(X0,A) ) ),
inference(fof_nnf,[status(thm)],[t2_funct_1_neg]) ).
fof(sk_t2_funct_1_neg,plain,
( ( ~ function(sK4)
| ~ relation(sK4) )
& ! [B,C,D] :
( D = C
| ~ in(ordered_pair(B,D),sK4)
| ~ in(ordered_pair(B,C),sK4) )
& ! [X0] :
( ordered_pair(sK5(X0),sK6(X0)) = X0
| ~ in(X0,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(A,sK4),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[nnf_32]) ).
cnf(c_76,negated_conjecture,
( ordered_pair(sK5(A),sK6(A)) = A
| ~ in(A,sK4) ),
inference(split_conjunct,[status(thm)],[sk_t2_funct_1_neg]) ).
cnf(c_77,negated_conjecture,
( C = B
| ~ in(ordered_pair(A,C),sK4)
| ~ in(ordered_pair(A,B),sK4) ),
inference(split_conjunct,[status(thm)],[sk_t2_funct_1_neg]) ).
cnf(c_78,negated_conjecture,
( ~ function(sK4)
| ~ relation(sK4) ),
inference(split_conjunct,[status(thm)],[sk_t2_funct_1_neg]) ).
cnf(c_141,plain,
( relation(sK4)
| ordered_pair(sK5(sK3(sK4)),sK6(sK3(sK4))) = sK3(sK4) ),
inference(resolve,[status(thm)],[c_76,c_73]) ).
cnf(c_146,plain,
( in(ordered_pair(sK0(sK4),sK2(sK4)),sK4)
| ~ relation(sK4) ),
inference(resolve,[status(thm)],[c_78,c_70]) ).
cnf(c_147,plain,
( in(ordered_pair(sK0(sK4),sK1(sK4)),sK4)
| ~ relation(sK4) ),
inference(resolve,[status(thm)],[c_78,c_69]) ).
cnf(c_1285,plain,
( ordered_pair(B,C) != sK3(A)
| relation(A) ),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_1286,plain,
( relation(sK4)
| relation(sK4) ),
inference(resolve,[status(thm)],[c_141,c_1285]) ).
cnf(c_524,plain,
relation(sK4),
inference(copy,[status(thm)],[c_1286]) ).
cnf(c_530,plain,
in(ordered_pair(sK0(sK4),sK1(sK4)),sK4),
inference(resolve,[status(thm)],[c_524,c_147]) ).
cnf(c_531,plain,
in(ordered_pair(sK0(sK4),sK2(sK4)),sK4),
inference(resolve,[status(thm)],[c_524,c_146]) ).
cnf(c_532,negated_conjecture,
~ function(sK4),
inference(resolve,[status(thm)],[c_524,c_78]) ).
cnf(c_541,negated_conjecture,
sK2(sK4) != sK1(sK4),
inference(resolve,[status(thm)],[c_71,c_532]) ).
cnf(c_1287,negated_conjecture,
( sK1(sK4) = A
| ~ in(ordered_pair(sK0(sK4),A),sK4) ),
inference(resolve,[status(thm)],[c_77,c_530]) ).
cnf(c_1288,plain,
sK1(sK4) != sK2(sK4),
inference(copy,[status(thm)],[c_541]) ).
cnf(c_1289,negated_conjecture,
~ in(ordered_pair(sK0(sK4),sK2(sK4)),sK4),
inference(resolve,[status(thm)],[c_1287,c_1288]) ).
cnf(c_1284,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_531,c_1289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:31:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 560797 was started by sandbox2 on n026,
% 0.09/0.37 % Sat Sep 26 08:31:56 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.82/0.57
% 0.82/0.57 % SZS status Theorem for theBenchmark
% 0.82/0.57
% 0.82/0.57 % Proof 1 at 0.12 (+ 0.05) seconds.
% 0.82/0.57 % Length of proof is 21.
% 0.82/0.57 % Level of proof is 6.
% 0.82/0.57 % Maximum clause weight is 32.000.
% 0.82/0.57 % Given clauses 419.
% 0.82/0.57
% 0.82/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------