%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:08:53 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.41s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 85 ( 18 unt; 7 def)
% Number of atoms : 203 ( 63 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 221 ( 103 ~; 111 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : member(X,singleton_set(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( X = Y
| ~ member(X,singleton_set(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : member(X,unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Y,X] : member(Y,unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( X = Z
| X = Y
| ~ member(X,unordered_pair(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
r1 != r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : member(X0,singleton_set(X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : member(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X,Z] :
( X = Z
| ! [Y] :
( X = Y
| ~ member(X,unordered_pair(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
r1 != r2,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,X2)
| X0 = singleton_set(X1)
| ~ member(X0,ordered_pair(X1,X2)) ),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f23,plain,
! [X0,X1] : member(unordered_pair(X0,X1),ordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f24,plain,
! [X0,X1] : member(singleton_set(X0),ordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f11]) ).
fof(f25,plain,
member(singleton_set(m1),ordered_pair(m2,r2)),
inference(paramodulation,[status(thm)],[f16,f24]) ).
fof(f27,plain,
member(unordered_pair(m1,r1),ordered_pair(m2,r2)),
inference(paramodulation,[status(thm)],[f16,f23]) ).
fof(f31,plain,
( unordered_pair(m1,r1) = unordered_pair(m2,r2)
| unordered_pair(m1,r1) = singleton_set(m2) ),
inference(resolution,[status(thm)],[f22,f27]) ).
fof(f33,plain,
( singleton_set(m1) = unordered_pair(m2,r2)
| singleton_set(m1) = singleton_set(m2) ),
inference(resolution,[status(thm)],[f22,f25]) ).
fof(f35,plain,
! [X0] :
( X0 = unordered_pair(m1,r1)
| X0 = singleton_set(m1)
| ~ member(X0,ordered_pair(m2,r2)) ),
inference(paramodulation,[status(thm)],[f16,f22]) ).
fof(f36,definition,
( sQ0_spl
<=> unordered_pair(m1,r1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ0_spl
| unordered_pair(m1,r1) = singleton_set(m2) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ1_spl
<=> unordered_pair(m1,r1) = unordered_pair(m2,r2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ1_spl
| unordered_pair(m1,r1) = unordered_pair(m2,r2) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f36,f39]) ).
fof(f43,definition,
( sQ2_spl
<=> singleton_set(m1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ2_spl
| singleton_set(m1) = singleton_set(m2) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f45,plain,
( sQ2_spl
| singleton_set(m1) != singleton_set(m2) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,definition,
( sQ3_spl
<=> singleton_set(m1) = unordered_pair(m2,r2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( ~ sQ3_spl
| singleton_set(m1) = unordered_pair(m2,r2) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f33,f43,f46]) ).
fof(f55,plain,
( ~ sQ2_spl
| member(m1,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[f44,f9]) ).
fof(f56,plain,
( ~ sQ2_spl
| m1 = m2 ),
inference(resolution,[status(thm)],[f55,f10]) ).
fof(f70,plain,
! [X0] :
( ~ sQ2_spl
| X0 = unordered_pair(m1,r1)
| X0 = singleton_set(m2)
| ~ member(X0,ordered_pair(m2,r2)) ),
inference(forward_demodulation,[status(thm)],[f44,f35]) ).
fof(f72,plain,
( ~ sQ2_spl
| unordered_pair(m2,r2) = unordered_pair(m1,r1)
| unordered_pair(m2,r2) = singleton_set(m2) ),
inference(resolution,[status(thm)],[f70,f23]) ).
fof(f78,definition,
( sQ5_spl
<=> unordered_pair(m2,r2) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ5_spl
| unordered_pair(m2,r2) = singleton_set(m2) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f72,f78,f39,f43]) ).
fof(f91,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| unordered_pair(m2,r1) = singleton_set(m2) ),
inference(forward_demodulation,[status(thm)],[f56,f37]) ).
fof(f96,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| member(r1,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[f91,f12]) ).
fof(f98,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| r1 = m2 ),
inference(resolution,[status(thm)],[f96,f10]) ).
fof(f100,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| unordered_pair(m2,m2) = singleton_set(m2) ),
inference(backward_demodulation,[status(thm)],[f98,f91]) ).
fof(f101,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| m2 != r2 ),
inference(backward_demodulation,[status(thm)],[f98,f17]) ).
fof(f111,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| unordered_pair(m2,r1) = unordered_pair(m2,r2) ),
inference(forward_demodulation,[status(thm)],[f56,f40]) ).
fof(f112,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| unordered_pair(m2,m2) = unordered_pair(m2,r2) ),
inference(forward_demodulation,[status(thm)],[f98,f111]) ).
fof(f113,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| singleton_set(m2) = unordered_pair(m2,r2) ),
inference(forward_demodulation,[status(thm)],[f100,f112]) ).
fof(f118,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| member(r2,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[f113,f12]) ).
fof(f120,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| r2 = m2 ),
inference(resolution,[status(thm)],[f118,f10]) ).
fof(f121,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f101]) ).
fof(f122,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f130,plain,
( ~ sQ5_spl
| member(r2,singleton_set(m2)) ),
inference(paramodulation,[status(thm)],[f79,f12]) ).
fof(f132,plain,
( ~ sQ5_spl
| r2 = m2 ),
inference(resolution,[status(thm)],[f130,f10]) ).
fof(f133,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f101]) ).
fof(f134,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f185,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| member(r1,unordered_pair(m2,r2)) ),
inference(paramodulation,[status(thm)],[f111,f12]) ).
fof(f192,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| r1 = r2
| r1 = m2 ),
inference(resolution,[status(thm)],[f185,f14]) ).
fof(f193,definition,
( sQ7_spl
<=> r1 = m2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ7_spl
| r1 = m2 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ8_spl
<=> r1 = r2 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ8_spl
| r1 = r2 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f192,f193,f196,f43,f39]) ).
fof(f201,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| unordered_pair(m2,m2) = unordered_pair(m2,r2) ),
inference(backward_demodulation,[status(thm)],[f194,f111]) ).
fof(f203,plain,
( ~ sQ7_spl
| m2 != r2 ),
inference(backward_demodulation,[status(thm)],[f194,f17]) ).
fof(f216,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| X0 = m2
| X0 = m2
| ~ member(X0,unordered_pair(m2,r2)) ),
inference(paramodulation,[status(thm)],[f201,f14]) ).
fof(f224,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| X0 = m2
| ~ member(X0,unordered_pair(m2,r2)) ),
inference(duplicate_literals_removal,[status(thm)],[f216]) ).
fof(f225,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| r2 = m2 ),
inference(resolution,[status(thm)],[f224,f12]) ).
fof(f227,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f203]) ).
fof(f228,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f229,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f17]) ).
fof(f230,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f237,plain,
( ~ sQ3_spl
| member(r2,singleton_set(m1)) ),
inference(paramodulation,[status(thm)],[f47,f12]) ).
fof(f238,plain,
( ~ sQ3_spl
| member(m2,singleton_set(m1)) ),
inference(paramodulation,[status(thm)],[f47,f11]) ).
fof(f239,plain,
( ~ sQ3_spl
| r2 = m1 ),
inference(resolution,[status(thm)],[f237,f10]) ).
fof(f242,plain,
( sQ2_spl
| ~ sQ3_spl
| singleton_set(r2) != singleton_set(m2) ),
inference(backward_demodulation,[status(thm)],[f239,f45]) ).
fof(f243,plain,
( ~ sQ3_spl
| member(m2,singleton_set(r2)) ),
inference(forward_demodulation,[status(thm)],[f239,f238]) ).
fof(f244,plain,
( ~ sQ3_spl
| m2 = r2 ),
inference(resolution,[status(thm)],[f243,f10]) ).
fof(f265,plain,
( sQ2_spl
| ~ sQ3_spl
| singleton_set(r2) != singleton_set(r2) ),
inference(forward_demodulation,[status(thm)],[f244,f242]) ).
fof(f266,plain,
( sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f265]) ).
fof(f267,plain,
( sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f268,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f49,f81,f122,f134,f199,f228,f230,f267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:42:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.16/0.38 % Drodi V4.1.1
% 0.16/0.41 % Refutation found
% 0.16/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.44 % Elapsed time: 0.065334 seconds
% 0.16/0.44 % CPU time: 0.188619 seconds
% 0.16/0.44 % Total memory used: 102.243 MB
% 0.16/0.44 % Net memory used: 101.731 MB
%------------------------------------------------------------------------------