%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU210+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:19:41 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 13 unt; 0 def)
% Number of atoms : 204 ( 28 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 243 ( 97 ~; 89 |; 42 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 146 ( 127 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B] :
( relation(B)
=> ~ ( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ~ ( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f35,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f55,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK3_skl(B,A),sK2_skl(B,A)),A)
| in(sK2_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK2_skl(B,A)),A)
| ~ in(sK2_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK1_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK1_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f63,plain,
! [A] : element(sK4_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(B,sK4_skl(A))],[f15]) ).
fof(f64,plain,
! [X0] : element(sK4_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f66,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f96,plain,
! [A,B,C] :
( ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f97,plain,
! [A,B,C] :
( ( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [C] :
( ( ! [A,B] :
( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& ! [A,B] :
( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f99,plain,
! [C] :
( ( ! [A,B] :
( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& ! [A,B] :
( ( in(sK11_skl(B,A,C),B)
& in(ordered_pair(A,sK11_skl(B,A,C)),C)
& in(sK11_skl(B,A,C),relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(D,sK11_skl(B,A,C))],[f98]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(X3,relation_rng(X0))
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f104,plain,
? [A,B] :
( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f105,plain,
? [B] :
( ? [A] :
( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set )
& relation(B) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
( relation_inverse_image(sK12_skl,sK13_skl) = empty_set
& subset(sK13_skl,relation_rng(sK12_skl))
& sK13_skl != empty_set
& relation(sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(B,sK12_skl),skolemize(A,sK13_skl)],[f105]) ).
fof(f107,plain,
relation(sK12_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
sK13_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
subset(sK13_skl,relation_rng(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
relation_inverse_image(sK12_skl,sK13_skl) = empty_set,
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f113,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f114,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f125,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f126,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f128,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f133,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f59]) ).
fof(f135,plain,
! [X0] :
( in(X0,relation_rng(sK12_skl))
| ~ in(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f51,f109]) ).
fof(f164,plain,
! [X0] :
( in(ordered_pair(sK1_skl(X0,relation_rng(sK12_skl),sK12_skl),X0),sK12_skl)
| ~ in(X0,relation_rng(sK12_skl)) ),
inference(resolution,[status(thm)],[f133,f107]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X1,X3),X0)
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f134]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),sK12_skl)
| in(X0,relation_inverse_image(sK12_skl,X1)) ),
inference(resolution,[status(thm)],[f191,f107]) ).
fof(f201,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[status(thm)],[f129,f66]) ).
fof(f228,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(sK12_skl))
| ~ in(X0,X1)
| in(sK1_skl(X0,relation_rng(sK12_skl),sK12_skl),relation_inverse_image(sK12_skl,X1)) ),
inference(resolution,[status(thm)],[f195,f164]) ).
fof(f313,plain,
! [X0,X1] :
( X1 = empty_set
| in(X0,X1)
| ~ element(X0,X1) ),
inference(resolution,[status(thm)],[f114,f126]) ).
fof(f342,plain,
! [X0] :
( X0 = empty_set
| in(sK4_skl(X0),X0) ),
inference(resolution,[status(thm)],[f313,f64]) ).
fof(f362,plain,
! [X0] :
( ~ in(X0,relation_rng(sK12_skl))
| ~ in(X0,sK13_skl)
| in(sK1_skl(X0,relation_rng(sK12_skl),sK12_skl),empty_set) ),
inference(paramodulation,[status(thm)],[f110,f228]) ).
fof(f363,plain,
! [X0] :
( ~ in(X0,relation_rng(sK12_skl))
| ~ in(X0,sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f362,f201]) ).
fof(f426,plain,
! [X0] : ~ in(X0,sK13_skl),
inference(forward_subsumption_resolution,[status(thm)],[f363,f135]) ).
fof(f427,plain,
sK13_skl = empty_set,
inference(resolution,[status(thm)],[f426,f342]) ).
fof(f431,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f427,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU210+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n014.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 05:58:05 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.51 % Refutation found
% 0.18/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.58 % Elapsed time: 0.120457 seconds
% 0.25/0.58 % CPU time: 0.165682 seconds
% 0.25/0.58 % Total memory used: 29.766 MB
% 0.25/0.58 % Net memory used: 29.666 MB
%------------------------------------------------------------------------------