%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:51:32 PM UTC 2026
% Result : Theorem 0.94s 1.21s
% Output : Proof 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 25 unt; 0 def)
% Number of atoms : 120 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 99 ( 40 ~; 34 |; 13 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 127 ( 6 sgn 77 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f15_nnf,plain,
! [A,B,C] :
( ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [C,A,B] :
( ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c17,plain,
( subset(relation_dom(X2),X0)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi11,axiom,
ifeq(relation_of2_as_subset(X0,X1,X2),true,subset(relation_dom(X0),X1),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
fof(f16,conjecture,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f16_neg,negated_conjecture,
~ ! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [A,B,C,D] :
( ~ relation_of2_as_subset(D,C,B)
& subset(relation_rng(D),B)
& relation_of2_as_subset(D,C,A) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( ~ relation_of2_as_subset(sk6,sk5,sk4)
& subset(relation_rng(sk6),sk4)
& relation_of2_as_subset(sk6,sk5,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5,sk6])],[f16_nnf]) ).
cnf(c19,plain,
relation_of2_as_subset(sk6,sk5,sk3),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi13,negated_conjecture,
relation_of2_as_subset(sk6,sk5,sk3) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h12,plain,
subset(relation_dom(sk6),sk5) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi13]) ).
fof(f14,axiom,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( subset(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( subset(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c16,plain,
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi10,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X2,X3),true,subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(c20,plain,
subset(relation_rng(sk6),sk4),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi14,negated_conjecture,
subset(relation_rng(sk6),sk4) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h57,plain,
subset(cartesian_product2(relation_dom(sk6),relation_rng(sk6)),cartesian_product2(sk5,sk4)) = true,
inference(hyper_resolution,[status(thm)],[hi10,h12,hi14]) ).
fof(f8,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f8_nnf,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [C,A,B] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi3,axiom,
ifeq(relation_of2_as_subset(X0,X1,X2),true,element(X0,powerset(cartesian_product2(X1,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h14,plain,
element(sk6,powerset(cartesian_product2(sk5,sk3))) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi13]) ).
fof(f0,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [C,A,B] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(element(X0,powerset(cartesian_product2(X1,X2))),true,relation(X0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h139,plain,
relation(sk6) = true,
inference(hyper_resolution,[status(thm)],[hi0,h14]) ).
fof(f18,axiom,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f18_nnf,plain,
! [A] :
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A] :
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c23,plain,
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi16,axiom,
ifeq(relation(X0),true,subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h165,plain,
subset(sk6,cartesian_product2(relation_dom(sk6),relation_rng(sk6))) = true,
inference(hyper_resolution,[status(thm)],[hi16,h139]) ).
fof(f17,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f17_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c22,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi15,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X2),true,subset(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h8711,plain,
subset(sk6,cartesian_product2(sk5,sk4)) = true,
inference(hyper_resolution,[status(thm)],[hi15,h165,h57]) ).
fof(f1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
<=> subset(C,cartesian_product2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
fof(f1_nnf,plain,
! [A,B,C] :
( ( ~ subset(C,cartesian_product2(A,B))
| relation_of2(C,A,B) )
& ( subset(C,cartesian_product2(A,B))
| ~ relation_of2(C,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [C,A,B] :
( ( ~ subset(C,cartesian_product2(A,B))
| relation_of2(C,A,B) )
& ( subset(C,cartesian_product2(A,B))
| ~ relation_of2(C,A,B) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
ifeq(subset(X0,cartesian_product2(X1,X2)),true,relation_of2(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h9663,plain,
relation_of2(sk6,sk5,sk4) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8711]) ).
fof(f12,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f12_nnf,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [C,A,B] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c14,plain,
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi8,axiom,
ifeq(relation_of2(X0,X1,X2),true,relation_of2_as_subset(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t10,plain,
relation_of2_as_subset(sk6,sk5,sk4) = true,
inference(hyper_resolution,[status(thm)],[hi8,h9663]) ).
cnf(t1613,plain,
relation_of2_as_subset(sk6,sk5,sk4) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(c21,plain,
~ relation_of2_as_subset(sk6,sk5,sk4),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
relation_of2_as_subset(sk6,sk5,sk4) != true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1613]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.36 % Computer : n018.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Thu Sep 24 13:29:19 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.94/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.94/1.21 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------