%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU151+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 : n012.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 02:19:24 PM UTC 2026
% Result : Theorem 0.02s 0.32s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% Number of atoms : 98 ( 75 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 107 ( 43 ~; 37 |; 25 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f9,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f12,plain,
( ! [A,B,C] :
( ( ( sK0_skl(C,B,A) = B
| sK0_skl(C,B,A) = A
| in(sK0_skl(C,B,A),C) )
& ( ( sK0_skl(C,B,A) != B
& sK0_skl(C,B,A) != A )
| ~ in(sK0_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f11]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| X3 = X1
| ~ in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f19,plain,
? [A,B,C,D] :
( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
? [A,D] :
( A != D
& ? [C] :
( A != C
& ? [B] : unordered_pair(A,B) = unordered_pair(C,D) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
( sK1_skl != sK2_skl
& sK1_skl != sK3_skl
& unordered_pair(sK1_skl,sK4_skl) = unordered_pair(sK3_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK1_skl),skolemize(D,sK2_skl),skolemize(C,sK3_skl),skolemize(B,sK4_skl)],[f20]) ).
fof(f22,plain,
unordered_pair(sK1_skl,sK4_skl) = unordered_pair(sK3_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
sK1_skl != sK3_skl,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,plain,
sK1_skl != sK2_skl,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f13]) ).
fof(f26,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f14]) ).
fof(f28,plain,
unordered_pair(sK1_skl,sK4_skl) = unordered_pair(sK2_skl,sK3_skl),
inference(backward_demodulation,[status(thm)],[f9,f22]) ).
fof(f33,plain,
unordered_pair(sK4_skl,sK1_skl) = unordered_pair(sK2_skl,sK3_skl),
inference(forward_demodulation,[status(thm)],[f9,f28]) ).
fof(f34,plain,
in(sK2_skl,unordered_pair(sK4_skl,sK1_skl)),
inference(paramodulation,[status(thm)],[f33,f26]) ).
fof(f35,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(paramodulation,[status(thm)],[f9,f26]) ).
fof(f49,plain,
( sK2_skl = sK1_skl
| sK2_skl = sK4_skl ),
inference(resolution,[status(thm)],[f25,f34]) ).
fof(f55,plain,
sK2_skl = sK4_skl,
inference(forward_subsumption_resolution,[status(thm)],[f49,f24]) ).
fof(f57,plain,
unordered_pair(sK4_skl,sK1_skl) = unordered_pair(sK4_skl,sK3_skl),
inference(backward_demodulation,[status(thm)],[f55,f33]) ).
fof(f58,plain,
sK1_skl != sK4_skl,
inference(backward_demodulation,[status(thm)],[f55,f24]) ).
fof(f59,plain,
! [X0] :
( X0 = sK1_skl
| X0 = sK4_skl
| ~ in(X0,unordered_pair(sK4_skl,sK3_skl)) ),
inference(paramodulation,[status(thm)],[f57,f25]) ).
fof(f62,plain,
in(sK1_skl,unordered_pair(sK4_skl,sK3_skl)),
inference(paramodulation,[status(thm)],[f57,f35]) ).
fof(f72,plain,
( sK3_skl = sK1_skl
| sK3_skl = sK4_skl ),
inference(resolution,[status(thm)],[f59,f35]) ).
fof(f74,plain,
sK3_skl = sK4_skl,
inference(forward_subsumption_resolution,[status(thm)],[f72,f23]) ).
fof(f79,plain,
in(sK1_skl,unordered_pair(sK4_skl,sK4_skl)),
inference(forward_demodulation,[status(thm)],[f74,f62]) ).
fof(f80,plain,
( sK1_skl = sK4_skl
| sK1_skl = sK4_skl ),
inference(resolution,[status(thm)],[f79,f25]) ).
fof(f82,plain,
sK1_skl = sK4_skl,
inference(duplicate_literals_removal,[status(thm)],[f80]) ).
fof(f83,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f82,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU151+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 21 05:52:52 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.02/0.32 % Refutation found
% 0.02/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.34 % Elapsed time: 0.041913 seconds
% 0.07/0.34 % CPU time: 0.092119 seconds
% 0.07/0.34 % Total memory used: 101.479 MB
% 0.07/0.34 % Net memory used: 101.015 MB
%------------------------------------------------------------------------------