%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET016-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:41:30 PM UTC 2026
% Result : Unsatisfiable 70.64s 9.57s
% Output : Proof 70.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 43 unt; 0 def)
% Number of atoms : 103 ( 59 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 102 ( 70 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-4 aty)
% Number of variables : 104 ( 26 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f167,negated_conjecture,
w != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_3) ).
fof(f167_nnf,plain,
w != y,
inference(nnf_transformation,[status(thm)],[f167]) ).
fof(f167_sk,plain,
w != y,
inference(skolemisation,[status(esa)],[f167_nnf]) ).
cnf(c167,plain,
w != y,
inference(cnf_transformation,[status(esa)],[f167_sk]) ).
cnf(t5,plain,
eq(w,y) = false,
inference(equality_encoding,[status(esa)],[c167]) ).
cnf(t1056,plain,
eq(w,y) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(f150,axiom,
( W = Y
| ~ member(W,universal_class)
| ordered_pair(W,X) != ordered_pair(Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
fof(f150_nnf,plain,
! [W,X,Y,Z] :
( W = Y
| ~ member(W,universal_class)
| ordered_pair(W,X) != ordered_pair(Y,Z) ),
inference(nnf_transformation,[status(thm)],[f150]) ).
fof(f150_sk,plain,
! [W,X,Y,Z] :
( W = Y
| ~ member(W,universal_class)
| ordered_pair(W,X) != ordered_pair(Y,Z) ),
inference(skolemisation,[status(esa)],[f150_nnf]) ).
cnf(c150,plain,
( X0 = X2
| ~ member(X0,universal_class)
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f150_sk]) ).
cnf(t146,plain,
ifeq(ordered_pair(X1,X2),ordered_pair(X3,X4),ifeq(member(X1,universal_class),true,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c150]) ).
cnf(t197,plain,
ifeq(ordered_pair(X1,X2),ordered_pair(X3,X4),ifeq(member(X1,universal_class),true,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t146]) ).
cnf(f165,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_1) ).
fof(f165_nnf,plain,
ordered_pair(w,x) = ordered_pair(y,z),
inference(nnf_transformation,[status(thm)],[f165]) ).
cnf(c165,plain,
ordered_pair(w,x) = ordered_pair(y,z),
inference(cnf_transformation,[status(esa)],[f165_nnf]) ).
cnf(t26,plain,
ordered_pair(y,z) = ordered_pair(w,x),
inference(equality_encoding,[status(esa)],[c165]) ).
cnf(t994,plain,
ordered_pair(w,x) = ordered_pair(y,z),
inference(orient,[status(thm)],[t26]) ).
cnf(t1005,plain,
X1 = ifeq(ordered_pair(y,z),ordered_pair(X1,X2),ifeq(member(w,universal_class),true,w,X1),X1),
inference(cp,[status(thm)],[t197,t994]) ).
cnf(f166,negated_conjecture,
member(w,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_2) ).
fof(f166_nnf,plain,
member(w,universal_class),
inference(nnf_transformation,[status(thm)],[f166]) ).
cnf(c166,plain,
member(w,universal_class),
inference(cnf_transformation,[status(esa)],[f166_nnf]) ).
cnf(t9,plain,
member(w,universal_class) = true,
inference(equality_encoding,[status(esa)],[c166]) ).
cnf(t249,plain,
member(w,universal_class) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t28729,plain,
X1 = ifeq(ordered_pair(y,z),ordered_pair(X1,X2),ifeq(true,true,w,X1),X1),
inference(step,[status(thm)],[t1005,t249]) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t187,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t28730,plain,
X1 = ifeq(ordered_pair(y,z),ordered_pair(X1,X2),w,X1),
inference(step,[status(thm)],[t28729,t187]) ).
cnf(t26233,plain,
ifeq(ordered_pair(y,z),ordered_pair(X1,X2),w,X1) = X1,
inference(orient,[status(thm)],[t28730]) ).
cnf(t26234,plain,
y = w,
inference(cp,[status(thm)],[t26233,t187]) ).
cnf(t26236,plain,
w = y,
inference(orient,[status(thm)],[t26234]) ).
cnf(t28732,plain,
eq(y,y) = false,
inference(step,[status(thm)],[t1056,t26236]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t686,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t28733,plain,
true = false,
inference(step,[status(thm)],[t28732,t686]) ).
cnf(t26238,plain,
true = false,
inference(rw,[status(thm)],[t28733]) ).
cnf(t26590,plain,
false = true,
inference(orient,[status(thm)],[t26238]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f101,axiom,
~ member(Y,intersection(complement(X),X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f101_nnf,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
~ member(X0,intersection(complement(X1),X1)),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(f102,axiom,
~ member(Z,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f102_nnf,plain,
! [Z] : ~ member(Z,null_class),
inference(nnf_transformation,[status(thm)],[f102]) ).
fof(f102_sk,plain,
! [Z] : ~ member(Z,null_class),
inference(skolemisation,[status(esa)],[f102_nnf]) ).
cnf(c102,plain,
~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f102_sk]) ).
cnf(f115,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f115_nnf,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f115]) ).
fof(f115_sk,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f115_nnf]) ).
cnf(c115,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f115_sk]) ).
cnf(f116,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f116_nnf,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( unordered_pair(X1,X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f117,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
fof(f117_nnf,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(nnf_transformation,[status(thm)],[f117]) ).
fof(f117_sk,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(skolemisation,[status(esa)],[f117_nnf]) ).
cnf(c117,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f117_sk]) ).
cnf(f122,axiom,
( singleton(X) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(f122_nnf,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( singleton(X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102,c115,c116,c117,c122,c167]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t26590]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET016-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 09:10:44 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 70.64/9.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 70.64/9.57 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------