%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU156+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 : n001.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 02:19:26 PM UTC 2026
% Result : Theorem 0.13s 0.49s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 94 ( 15 unt; 11 def)
% Number of atoms : 200 ( 117 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 192 ( 86 ~; 85 |; 6 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 95 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [A,D] :
( A = D
| ! [C] :
( A = C
| ! [B] : unordered_pair(A,B) != unordered_pair(C,D) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
? [A,B,C,D] :
( ( B != D
| A != C )
& ordered_pair(A,B) = ordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
( ( sK3_skl != sK5_skl
| sK2_skl != sK4_skl )
& ordered_pair(sK2_skl,sK3_skl) = ordered_pair(sK4_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f29]) ).
fof(f31,plain,
ordered_pair(sK2_skl,sK3_skl) = ordered_pair(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
( sK3_skl != sK5_skl
| sK2_skl != sK4_skl ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
! [A,B] :
( A = B
| ! [C] : singleton(A) != unordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f40,plain,
! [B,C] :
( B = C
| ! [A] : singleton(A) != unordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,definition,
( sQ0_spl
<=> sK2_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ0_spl
| sK2_skl = sK4_skl ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f44,plain,
( sQ0_spl
| sK2_skl != sK4_skl ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
( sQ1_spl
<=> sK3_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( sQ1_spl
| sK3_skl != sK5_skl ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f42,f45]) ).
fof(f125,plain,
! [X0] : ordered_pair(X0,X0) = unordered_pair(singleton(X0),singleton(X0)),
inference(paramodulation,[status(thm)],[f33,f18]) ).
fof(f132,plain,
! [X0] : ordered_pair(X0,X0) = singleton(singleton(X0)),
inference(forward_demodulation,[status(thm)],[f33,f125]) ).
fof(f138,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f17]) ).
fof(f178,plain,
! [X0,X1,X2,X3] :
( unordered_pair(X0,X1) = X3
| unordered_pair(X0,X1) = X2
| ordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f187,plain,
! [X0,X1,X2,X3] :
( X0 = singleton(X2)
| X0 = unordered_pair(X2,X3)
| unordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f200,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,X2)
| singleton(X0) != ordered_pair(X1,X2) ),
inference(paramodulation,[status(thm)],[f18,f38]) ).
fof(f201,plain,
! [X0,X1,X2] :
( X0 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(paramodulation,[status(thm)],[f17,f38]) ).
fof(f203,plain,
! [X0,X1] :
( X0 = X1
| singleton(X0) != singleton(X1) ),
inference(paramodulation,[status(thm)],[f33,f38]) ).
fof(f270,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(paramodulation,[status(thm)],[f17,f138]) ).
fof(f298,plain,
! [X0,X1,X2] :
( unordered_pair(X1,X2) = singleton(X1)
| singleton(X0) != ordered_pair(X1,X2) ),
inference(paramodulation,[status(thm)],[f18,f41]) ).
fof(f421,plain,
! [X0,X1] :
( unordered_pair(sK4_skl,sK5_skl) = X1
| unordered_pair(sK4_skl,sK5_skl) = X0
| ordered_pair(sK2_skl,sK3_skl) != unordered_pair(X0,X1) ),
inference(paramodulation,[status(thm)],[f31,f178]) ).
fof(f570,plain,
! [X0,X1] :
( X0 = singleton(sK4_skl)
| X0 = unordered_pair(sK4_skl,sK5_skl)
| unordered_pair(X0,X1) != ordered_pair(sK2_skl,sK3_skl) ),
inference(paramodulation,[status(thm)],[f31,f187]) ).
fof(f596,plain,
( unordered_pair(sK4_skl,sK5_skl) = unordered_pair(sK3_skl,sK2_skl)
| unordered_pair(sK4_skl,sK5_skl) = singleton(sK2_skl) ),
inference(resolution,[status(thm)],[f421,f270]) ).
fof(f615,definition,
( sQ21_spl
<=> unordered_pair(sK4_skl,sK5_skl) = singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( ~ sQ21_spl
| unordered_pair(sK4_skl,sK5_skl) = singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f615]) ).
fof(f618,definition,
( sQ22_spl
<=> unordered_pair(sK4_skl,sK5_skl) = unordered_pair(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f619,plain,
( ~ sQ22_spl
| unordered_pair(sK4_skl,sK5_skl) = unordered_pair(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f618]) ).
fof(f621,plain,
( sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f596,f615,f618]) ).
fof(f678,plain,
( ~ sQ21_spl
| sK2_skl = sK4_skl ),
inference(resolution,[status(thm)],[f616,f38]) ).
fof(f684,plain,
! [X0] :
( ~ sQ21_spl
| sK4_skl = sK5_skl
| singleton(X0) != singleton(sK2_skl) ),
inference(paramodulation,[status(thm)],[f616,f41]) ).
fof(f703,plain,
( ~ sQ21_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f678,f44]) ).
fof(f704,plain,
( ~ sQ21_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f703]) ).
fof(f733,definition,
( sQ40_spl
<=> unordered_pair(sK2_skl,sK3_skl) = singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f734,plain,
( ~ sQ40_spl
| unordered_pair(sK2_skl,sK3_skl) = singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f733]) ).
fof(f739,definition,
! [X0] :
( sQ41_spl
<=> singleton(X0) != singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f740,plain,
! [X0] :
( ~ sQ41_spl
| singleton(X0) != singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f742,definition,
( sQ42_spl
<=> sK4_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f743,plain,
( ~ sQ42_spl
| sK4_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f742]) ).
fof(f745,plain,
( ~ sQ21_spl
| sQ42_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f684,f739,f742,f615]) ).
fof(f760,plain,
( sQ1_spl
| ~ sQ42_spl
| ~ sQ0_spl
| sK3_skl != sK2_skl ),
inference(backward_demodulation,[status(thm)],[f761,f47]) ).
fof(f761,plain,
( ~ sQ42_spl
| ~ sQ0_spl
| sK2_skl = sK5_skl ),
inference(forward_demodulation,[status(thm)],[f43,f743]) ).
fof(f845,plain,
( ~ sQ42_spl
| ordered_pair(sK2_skl,sK3_skl) = ordered_pair(sK4_skl,sK4_skl) ),
inference(backward_demodulation,[status(thm)],[f743,f31]) ).
fof(f847,plain,
( ~ sQ42_spl
| ordered_pair(sK2_skl,sK3_skl) = singleton(singleton(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f132,f845]) ).
fof(f853,plain,
! [X0] :
( ~ sQ42_spl
| unordered_pair(sK2_skl,sK3_skl) = singleton(sK2_skl)
| singleton(X0) != singleton(singleton(sK4_skl)) ),
inference(paramodulation,[status(thm)],[f847,f298]) ).
fof(f863,definition,
! [X0] :
( sQ43_spl
<=> singleton(X0) != singleton(singleton(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f864,plain,
! [X0] :
( ~ sQ43_spl
| singleton(X0) != singleton(singleton(sK4_skl)) ),
inference(component_clause,[status(thm)],[f863]) ).
fof(f866,plain,
( ~ sQ42_spl
| sQ40_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f853,f863,f733,f742]) ).
fof(f889,definition,
( sQ45_spl
<=> sK2_skl = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f890,plain,
( ~ sQ45_spl
| sK2_skl = sK3_skl ),
inference(component_clause,[status(thm)],[f889]) ).
fof(f900,plain,
( ~ sQ45_spl
| ordered_pair(sK2_skl,sK2_skl) = ordered_pair(sK4_skl,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f890,f31]) ).
fof(f901,plain,
( ~ sQ45_spl
| singleton(singleton(sK2_skl)) = ordered_pair(sK4_skl,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f132,f900]) ).
fof(f905,plain,
( ~ sQ45_spl
| singleton(sK2_skl) = unordered_pair(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f901,f200]) ).
fof(f917,plain,
( ~ sQ45_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f905,f615,f889]) ).
fof(f918,definition,
! [X0] :
( sQ46_spl
<=> singleton(X0) != singleton(singleton(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f919,plain,
! [X0] :
( ~ sQ46_spl
| singleton(X0) != singleton(singleton(sK2_skl)) ),
inference(component_clause,[status(thm)],[f918]) ).
fof(f1005,plain,
( ~ sQ43_spl
| $false ),
inference(equality_resolution,[status(thm)],[f864]) ).
fof(f1006,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f1005]) ).
fof(f1007,plain,
( ~ sQ46_spl
| $false ),
inference(equality_resolution,[status(thm)],[f919]) ).
fof(f1008,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f1007]) ).
fof(f1009,plain,
( ~ sQ40_spl
| sK2_skl = sK3_skl ),
inference(resolution,[status(thm)],[f734,f201]) ).
fof(f1028,plain,
( ~ sQ40_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1009,f889,f733]) ).
fof(f1049,plain,
( sQ1_spl
| ~ sQ42_spl
| ~ sQ0_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f760,f889,f42,f742,f45]) ).
fof(f1133,plain,
( ~ sQ41_spl
| $false ),
inference(equality_resolution,[status(thm)],[f740]) ).
fof(f1134,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f1133]) ).
fof(f1135,plain,
( singleton(sK2_skl) = singleton(sK4_skl)
| singleton(sK2_skl) = unordered_pair(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f570,f270]) ).
fof(f1151,definition,
( sQ49_spl
<=> singleton(sK2_skl) = singleton(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1152,plain,
( ~ sQ49_spl
| singleton(sK2_skl) = singleton(sK4_skl) ),
inference(component_clause,[status(thm)],[f1151]) ).
fof(f1154,plain,
( sQ49_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1135,f615,f1151]) ).
fof(f1165,plain,
( ~ sQ49_spl
| sK2_skl = sK4_skl ),
inference(resolution,[status(thm)],[f1152,f203]) ).
fof(f1180,plain,
( ~ sQ49_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1165,f42,f1151]) ).
fof(f1461,plain,
( ~ sQ22_spl
| ~ sQ0_spl
| unordered_pair(sK2_skl,sK5_skl) = unordered_pair(sK3_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f43,f619]) ).
fof(f1465,plain,
( ~ sQ22_spl
| ~ sQ0_spl
| sK3_skl = sK5_skl
| sK3_skl = sK2_skl ),
inference(resolution,[status(thm)],[f1461,f28]) ).
fof(f1499,plain,
( ~ sQ22_spl
| ~ sQ0_spl
| sQ1_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1465,f889,f45,f42,f618]) ).
fof(f1514,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f621,f704,f745,f866,f917,f1006,f1008,f1028,f1049,f1134,f1154,f1180,f1499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:59:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.49 % Refutation found
% 0.13/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.50 % Elapsed time: 0.134823 seconds
% 0.13/0.50 % CPU time: 0.802034 seconds
% 0.13/0.50 % Total memory used: 124.762 MB
% 0.13/0.50 % Net memory used: 123.331 MB
%------------------------------------------------------------------------------