%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /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 : Thu Sep 24 02:19:57 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 89 ( 88 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 112 ( 49 ~; 41 |; 14 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 88 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,conjecture,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,plain,
? [A,B] :
( pair_second(ordered_pair(A,B)) != B
| pair_first(ordered_pair(A,B)) != A ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
( ? [A,B] : pair_second(ordered_pair(A,B)) != B
| ? [A,B] : pair_first(ordered_pair(A,B)) != A ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
( pair_second(ordered_pair(sK5_skl,sK6_skl)) != sK6_skl
| pair_first(ordered_pair(sK3_skl,sK4_skl)) != sK3_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f44]) ).
fof(f46,plain,
( pair_second(ordered_pair(sK5_skl,sK6_skl)) != sK6_skl
| pair_first(ordered_pair(sK3_skl,sK4_skl)) != sK3_skl ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [A] :
( ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( B = C
| A != ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( B != C
& A = ordered_pair(C,D) )
| B = pair_first(A) )
& ( ! [C,D] :
( B = C
| A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( B != C
& ? [D] : A = ordered_pair(C,D) )
| B = pair_first(A) )
& ! [B] :
( ! [C] :
( B = C
| ! [D] : A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ! [B] :
( ( B != sK7_skl(B,A)
& A = ordered_pair(sK7_skl(B,A),sK8_skl(B,A)) )
| B = pair_first(A) )
& ! [B] :
( ! [C] :
( B = C
| ! [D] : A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(C,sK7_skl(B,A)),skolemize(D,sK8_skl(B,A))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 = X4
| X0 != ordered_pair(X4,X5)
| X3 != pair_first(X0)
| X0 != ordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
! [A] :
( ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( B = D
| A != ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( B != D
& A = ordered_pair(C,D) )
| B = pair_second(A) )
& ( ! [C,D] :
( B = D
| A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(NNF_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [A] :
( ( ! [B] :
( ? [D] :
( B != D
& ? [C] : A = ordered_pair(C,D) )
| B = pair_second(A) )
& ! [B] :
( ! [D] :
( B = D
| ! [C] : A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
! [A] :
( ( ! [B] :
( ( B != sK9_skl(B,A)
& A = ordered_pair(sK10_skl(B,A),sK9_skl(B,A)) )
| B = pair_second(A) )
& ! [B] :
( ! [D] :
( B = D
| ! [C] : A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(D,sK9_skl(B,A)),skolemize(C,sK10_skl(B,A))],[f56]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 = X5
| X0 != ordered_pair(X4,X5)
| X3 != pair_second(X0)
| X0 != ordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( pair_first(ordered_pair(X0,X1)) = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( pair_second(ordered_pair(X0,X1)) = X3
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f67,plain,
! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
inference(equality_resolution,[status(thm)],[f61]) ).
fof(f68,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(equality_resolution,[status(thm)],[f64]) ).
fof(f69,plain,
( pair_second(ordered_pair(sK5_skl,sK6_skl)) != sK6_skl
| sK3_skl != sK3_skl ),
inference(backward_demodulation,[status(thm)],[f67,f46]) ).
fof(f71,plain,
pair_second(ordered_pair(sK5_skl,sK6_skl)) != sK6_skl,
inference(trivial_equality_resolution,[status(thm)],[f69]) ).
fof(f73,plain,
sK6_skl != sK6_skl,
inference(forward_demodulation,[status(thm)],[f68,f71]) ).
fof(f74,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n026.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 06:07:36 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.054366 seconds
% 0.12/0.43 % CPU time: 0.149137 seconds
% 0.12/0.43 % Total memory used: 80.337 MB
% 0.12/0.43 % Net memory used: 79.881 MB
%------------------------------------------------------------------------------