%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:11:00 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 157 ( 121 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 181 ( 72 ~; 76 |; 27 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [A,B,C] :
( ( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| subset(A,unordered_pair(B,C)) )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
( ! [A,B,C] :
( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| subset(A,unordered_pair(B,C)) )
& ! [A,B,C] :
( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,X2)
| X0 = singleton(X2)
| X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( X0 != empty_set
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
! [X0,X1,X2] :
( X0 != singleton(X2)
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f24,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f27,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
? [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<~> ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
? [A,B,C] :
( ( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| set_difference(A,unordered_pair(B,C)) != empty_set )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| set_difference(A,unordered_pair(B,C)) = empty_set ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
( ( ( sK2_skl != unordered_pair(sK3_skl,sK4_skl)
& sK2_skl != singleton(sK4_skl)
& sK2_skl != singleton(sK3_skl)
& sK2_skl != empty_set )
| set_difference(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) != empty_set )
& ( sK2_skl = unordered_pair(sK3_skl,sK4_skl)
| sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| set_difference(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f31]) ).
fof(f33,plain,
( sK2_skl = unordered_pair(sK3_skl,sK4_skl)
| sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| set_difference(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) = empty_set ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( sK2_skl != empty_set
| set_difference(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) != empty_set ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
( sK2_skl != singleton(sK3_skl)
| set_difference(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) != empty_set ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
( sK2_skl != singleton(sK4_skl)
| set_difference(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) != empty_set ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f37,plain,
( sK2_skl != unordered_pair(sK3_skl,sK4_skl)
| set_difference(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) != empty_set ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f38,plain,
! [X0,X1] : subset(empty_set,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f17]) ).
fof(f40,plain,
! [X0,X1] : subset(singleton(X0),unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f56,plain,
( sK2_skl = unordered_pair(sK3_skl,sK4_skl)
| sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f28,f33]) ).
fof(f63,plain,
( sK2_skl != singleton(sK4_skl)
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f29,f36]) ).
fof(f64,plain,
( sK2_skl != singleton(sK3_skl)
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f29,f35]) ).
fof(f65,plain,
( sK2_skl != empty_set
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f29,f34]) ).
fof(f73,plain,
( ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))
| sK2_skl != unordered_pair(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f37,f29]) ).
fof(f75,plain,
( sK2_skl = unordered_pair(sK3_skl,sK4_skl)
| sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f15]) ).
fof(f88,plain,
( sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| ~ subset(sK2_skl,sK2_skl)
| sK2_skl != unordered_pair(sK3_skl,sK4_skl) ),
inference(paramodulation,[status(thm)],[f75,f73]) ).
fof(f89,plain,
( sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| ~ subset(sK2_skl,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f75]) ).
fof(f90,plain,
( sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f25]) ).
fof(f91,plain,
! [X0] :
( sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| subset(sK2_skl,unordered_pair(X0,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f90,f40]) ).
fof(f95,plain,
( sK2_skl != singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set ),
inference(resolution,[status(thm)],[f91,f63]) ).
fof(f100,plain,
( sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f90]) ).
fof(f103,plain,
! [X0] :
( sK2_skl = empty_set
| subset(sK2_skl,unordered_pair(sK3_skl,X0)) ),
inference(paramodulation,[status(thm)],[f100,f39]) ).
fof(f109,plain,
( sK2_skl != singleton(sK3_skl)
| sK2_skl = empty_set ),
inference(resolution,[status(thm)],[f103,f64]) ).
fof(f115,plain,
sK2_skl = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[f109,f100]) ).
fof(f124,plain,
( empty_set != empty_set
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f115,f65]) ).
fof(f135,plain,
( empty_set != empty_set
| ~ subset(empty_set,unordered_pair(sK3_skl,sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f115,f124]) ).
fof(f136,plain,
~ subset(empty_set,unordered_pair(sK3_skl,sK4_skl)),
inference(trivial_equality_resolution,[status(thm)],[f135]) ).
fof(f137,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f136,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:45:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.056646 seconds
% 0.14/0.43 % CPU time: 0.160638 seconds
% 0.14/0.43 % Total memory used: 102.096 MB
% 0.14/0.43 % Net memory used: 101.718 MB
%------------------------------------------------------------------------------