%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU156+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 : n018.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 0.14s 0.45s
% Output : CNFRefutation 0.14s
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,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(f24,plain,
! [A,D] :
( A = D
| ! [C] :
( A = C
| ! [B] : unordered_pair(A,B) != unordered_pair(C,D) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
? [A,B,C,D] :
( ( B != D
| A != C )
& ordered_pair(A,B) = ordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f27,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)],[f26]) ).
fof(f28,plain,
ordered_pair(sK2_skl,sK3_skl) = ordered_pair(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( sK3_skl != sK5_skl
| sK2_skl != sK4_skl ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
! [A,B] :
( A = B
| ! [C] : singleton(A) != unordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f37,plain,
! [B,C] :
( B = C
| ! [A] : singleton(A) != unordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,definition,
( sQ0_spl
<=> sK2_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ0_spl
| sK2_skl = sK4_skl ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f41,plain,
( sQ0_spl
| sK2_skl != sK4_skl ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
( sQ1_spl
<=> sK3_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( sQ1_spl
| sK3_skl != sK5_skl ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f39,f42]) ).
fof(f122,plain,
! [X0] : ordered_pair(X0,X0) = unordered_pair(singleton(X0),singleton(X0)),
inference(paramodulation,[status(thm)],[f30,f15]) ).
fof(f129,plain,
! [X0] : ordered_pair(X0,X0) = singleton(singleton(X0)),
inference(forward_demodulation,[status(thm)],[f30,f122]) ).
fof(f135,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f175,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)],[f15,f25]) ).
fof(f184,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)],[f15,f25]) ).
fof(f197,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,X2)
| singleton(X0) != ordered_pair(X1,X2) ),
inference(paramodulation,[status(thm)],[f15,f35]) ).
fof(f198,plain,
! [X0,X1,X2] :
( X0 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(paramodulation,[status(thm)],[f14,f35]) ).
fof(f200,plain,
! [X0,X1] :
( X0 = X1
| singleton(X0) != singleton(X1) ),
inference(paramodulation,[status(thm)],[f30,f35]) ).
fof(f267,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(paramodulation,[status(thm)],[f14,f135]) ).
fof(f295,plain,
! [X0,X1,X2] :
( unordered_pair(X1,X2) = singleton(X1)
| singleton(X0) != ordered_pair(X1,X2) ),
inference(paramodulation,[status(thm)],[f15,f38]) ).
fof(f418,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)],[f28,f175]) ).
fof(f567,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)],[f28,f184]) ).
fof(f593,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)],[f418,f267]) ).
fof(f612,definition,
( sQ21_spl
<=> unordered_pair(sK4_skl,sK5_skl) = singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( ~ sQ21_spl
| unordered_pair(sK4_skl,sK5_skl) = singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f612]) ).
fof(f615,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(f616,plain,
( ~ sQ22_spl
| unordered_pair(sK4_skl,sK5_skl) = unordered_pair(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f615]) ).
fof(f618,plain,
( sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f593,f612,f615]) ).
fof(f675,plain,
( ~ sQ21_spl
| sK2_skl = sK4_skl ),
inference(resolution,[status(thm)],[f613,f35]) ).
fof(f681,plain,
! [X0] :
( ~ sQ21_spl
| sK4_skl = sK5_skl
| singleton(X0) != singleton(sK2_skl) ),
inference(paramodulation,[status(thm)],[f613,f38]) ).
fof(f700,plain,
( ~ sQ21_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f675,f41]) ).
fof(f701,plain,
( ~ sQ21_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f700]) ).
fof(f730,definition,
( sQ40_spl
<=> unordered_pair(sK2_skl,sK3_skl) = singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( ~ sQ40_spl
| unordered_pair(sK2_skl,sK3_skl) = singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f736,definition,
! [X0] :
( sQ41_spl
<=> singleton(X0) != singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f737,plain,
! [X0] :
( ~ sQ41_spl
| singleton(X0) != singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f736]) ).
fof(f739,definition,
( sQ42_spl
<=> sK4_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f740,plain,
( ~ sQ42_spl
| sK4_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f742,plain,
( ~ sQ21_spl
| sQ42_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f681,f736,f739,f612]) ).
fof(f757,plain,
( sQ1_spl
| ~ sQ42_spl
| ~ sQ0_spl
| sK3_skl != sK2_skl ),
inference(backward_demodulation,[status(thm)],[f758,f44]) ).
fof(f758,plain,
( ~ sQ42_spl
| ~ sQ0_spl
| sK2_skl = sK5_skl ),
inference(forward_demodulation,[status(thm)],[f40,f740]) ).
fof(f842,plain,
( ~ sQ42_spl
| ordered_pair(sK2_skl,sK3_skl) = ordered_pair(sK4_skl,sK4_skl) ),
inference(backward_demodulation,[status(thm)],[f740,f28]) ).
fof(f844,plain,
( ~ sQ42_spl
| ordered_pair(sK2_skl,sK3_skl) = singleton(singleton(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f129,f842]) ).
fof(f850,plain,
! [X0] :
( ~ sQ42_spl
| unordered_pair(sK2_skl,sK3_skl) = singleton(sK2_skl)
| singleton(X0) != singleton(singleton(sK4_skl)) ),
inference(paramodulation,[status(thm)],[f844,f295]) ).
fof(f860,definition,
! [X0] :
( sQ43_spl
<=> singleton(X0) != singleton(singleton(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f861,plain,
! [X0] :
( ~ sQ43_spl
| singleton(X0) != singleton(singleton(sK4_skl)) ),
inference(component_clause,[status(thm)],[f860]) ).
fof(f863,plain,
( ~ sQ42_spl
| sQ40_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f850,f860,f730,f739]) ).
fof(f886,definition,
( sQ45_spl
<=> sK2_skl = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f887,plain,
( ~ sQ45_spl
| sK2_skl = sK3_skl ),
inference(component_clause,[status(thm)],[f886]) ).
fof(f897,plain,
( ~ sQ45_spl
| ordered_pair(sK2_skl,sK2_skl) = ordered_pair(sK4_skl,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f887,f28]) ).
fof(f898,plain,
( ~ sQ45_spl
| singleton(singleton(sK2_skl)) = ordered_pair(sK4_skl,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f129,f897]) ).
fof(f902,plain,
( ~ sQ45_spl
| singleton(sK2_skl) = unordered_pair(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f898,f197]) ).
fof(f914,plain,
( ~ sQ45_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f902,f612,f886]) ).
fof(f915,definition,
! [X0] :
( sQ46_spl
<=> singleton(X0) != singleton(singleton(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f916,plain,
! [X0] :
( ~ sQ46_spl
| singleton(X0) != singleton(singleton(sK2_skl)) ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f1002,plain,
( ~ sQ43_spl
| $false ),
inference(equality_resolution,[status(thm)],[f861]) ).
fof(f1003,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f1002]) ).
fof(f1004,plain,
( ~ sQ46_spl
| $false ),
inference(equality_resolution,[status(thm)],[f916]) ).
fof(f1005,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f1004]) ).
fof(f1006,plain,
( ~ sQ40_spl
| sK2_skl = sK3_skl ),
inference(resolution,[status(thm)],[f731,f198]) ).
fof(f1025,plain,
( ~ sQ40_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1006,f886,f730]) ).
fof(f1046,plain,
( sQ1_spl
| ~ sQ42_spl
| ~ sQ0_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f757,f886,f39,f739,f42]) ).
fof(f1130,plain,
( ~ sQ41_spl
| $false ),
inference(equality_resolution,[status(thm)],[f737]) ).
fof(f1131,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f1130]) ).
fof(f1132,plain,
( singleton(sK2_skl) = singleton(sK4_skl)
| singleton(sK2_skl) = unordered_pair(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f567,f267]) ).
fof(f1148,definition,
( sQ49_spl
<=> singleton(sK2_skl) = singleton(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1149,plain,
( ~ sQ49_spl
| singleton(sK2_skl) = singleton(sK4_skl) ),
inference(component_clause,[status(thm)],[f1148]) ).
fof(f1151,plain,
( sQ49_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1132,f612,f1148]) ).
fof(f1162,plain,
( ~ sQ49_spl
| sK2_skl = sK4_skl ),
inference(resolution,[status(thm)],[f1149,f200]) ).
fof(f1177,plain,
( ~ sQ49_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1162,f39,f1148]) ).
fof(f1458,plain,
( ~ sQ22_spl
| ~ sQ0_spl
| unordered_pair(sK2_skl,sK5_skl) = unordered_pair(sK3_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f40,f616]) ).
fof(f1462,plain,
( ~ sQ22_spl
| ~ sQ0_spl
| sK3_skl = sK5_skl
| sK3_skl = sK2_skl ),
inference(resolution,[status(thm)],[f1458,f25]) ).
fof(f1496,plain,
( ~ sQ22_spl
| ~ sQ0_spl
| sQ1_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1462,f886,f42,f39,f615]) ).
fof(f1511,plain,
$false,
inference(sat_refutation,[status(thm)],[f45,f618,f701,f742,f863,f914,f1003,f1005,f1025,f1046,f1131,f1151,f1177,f1496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:55:28 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.14/0.45 % Refutation found
% 0.14/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.48 % Elapsed time: 0.107423 seconds
% 0.14/0.48 % CPU time: 0.520168 seconds
% 0.14/0.48 % Total memory used: 116.416 MB
% 0.14/0.48 % Net memory used: 115.511 MB
%------------------------------------------------------------------------------