%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /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 : Thu Sep 24 02:19:25 PM UTC 2026
% Result : Theorem 0.10s 0.61s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 13 unt; 5 def)
% Number of atoms : 133 ( 79 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 148 ( 62 ~; 54 |; 25 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 61 ( 51 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f10,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
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) )
& ( ! [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(f12,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)],[f11]) ).
fof(f13,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))],[f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| X3 = X1
| ~ in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f24,plain,
? [A,B,C,D] :
( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
? [A,D] :
( A != D
& ? [C] :
( A != C
& ? [B] : unordered_pair(A,B) = unordered_pair(C,D) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
( sK3_skl != sK4_skl
& sK3_skl != sK5_skl
& unordered_pair(sK3_skl,sK6_skl) = unordered_pair(sK5_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(D,sK4_skl),skolemize(C,sK5_skl),skolemize(B,sK6_skl)],[f25]) ).
fof(f27,plain,
unordered_pair(sK3_skl,sK6_skl) = unordered_pair(sK5_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
sK3_skl != sK5_skl,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
sK3_skl != sK4_skl,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f14]) ).
fof(f31,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f15]) ).
fof(f33,plain,
unordered_pair(sK5_skl,sK4_skl) = unordered_pair(sK6_skl,sK3_skl),
inference(paramodulation,[status(thm)],[f27,f10]) ).
fof(f42,plain,
in(sK5_skl,unordered_pair(sK6_skl,sK3_skl)),
inference(paramodulation,[status(thm)],[f33,f31]) ).
fof(f43,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(paramodulation,[status(thm)],[f10,f31]) ).
fof(f45,plain,
in(sK4_skl,unordered_pair(sK6_skl,sK3_skl)),
inference(paramodulation,[status(thm)],[f33,f43]) ).
fof(f58,plain,
( sK4_skl = sK3_skl
| sK4_skl = sK6_skl ),
inference(resolution,[status(thm)],[f30,f45]) ).
fof(f59,plain,
( sK5_skl = sK3_skl
| sK5_skl = sK6_skl ),
inference(resolution,[status(thm)],[f30,f42]) ).
fof(f65,definition,
( sQ0_spl
<=> sK4_skl = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ0_spl
| sK4_skl = sK6_skl ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,definition,
( sQ1_spl
<=> sK4_skl = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( ~ sQ1_spl
| sK4_skl = sK3_skl ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f65,f68]) ).
fof(f72,definition,
( sQ2_spl
<=> sK5_skl = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( ~ sQ2_spl
| sK5_skl = sK6_skl ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
( sQ3_spl
<=> sK5_skl = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ3_spl
| sK5_skl = sK3_skl ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f59,f72,f75]) ).
fof(f81,plain,
( ~ sQ2_spl
| unordered_pair(sK6_skl,sK4_skl) = unordered_pair(sK6_skl,sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f73,f33]) ).
fof(f85,plain,
( ~ sQ0_spl
| sK3_skl != sK6_skl ),
inference(backward_demodulation,[status(thm)],[f66,f29]) ).
fof(f86,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| unordered_pair(sK6_skl,sK6_skl) = unordered_pair(sK6_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f66,f81]) ).
fof(f90,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| in(sK3_skl,unordered_pair(sK6_skl,sK6_skl)) ),
inference(paramodulation,[status(thm)],[f86,f43]) ).
fof(f92,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sK3_skl = sK6_skl
| sK3_skl = sK6_skl ),
inference(resolution,[status(thm)],[f90,f30]) ).
fof(f94,definition,
( sQ4_spl
<=> sK3_skl = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f92,f94,f65,f72]) ).
fof(f116,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f29]) ).
fof(f117,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f118,plain,
( ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f85,f94,f65]) ).
fof(f123,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f28]) ).
fof(f124,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f123]) ).
fof(f125,plain,
$false,
inference(sat_refutation,[status(thm)],[f71,f78,f97,f117,f118,f124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n020.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 05:54:03 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.58 % Drodi V4.1.1
% 0.10/0.61 % Refutation found
% 0.10/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.63 % Elapsed time: 0.054591 seconds
% 0.15/0.63 % CPU time: 0.149235 seconds
% 0.15/0.63 % Total memory used: 101.509 MB
% 0.15/0.63 % Net memory used: 101.091 MB
%------------------------------------------------------------------------------