%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET296-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 02:43:03 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.85s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 24 unt; 0 def)
% Number of atoms : 40 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 22 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f112,negated_conjecture,
domain_of(inverse(x)) != range_of(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_inverse_1) ).
fof(f112_nnf,plain,
domain_of(inverse(x)) != range_of(x),
inference(nnf_transformation,[status(thm)],[f112]) ).
fof(f112_sk,plain,
domain_of(inverse(x)) != range_of(x),
inference(skolemisation,[status(esa)],[f112_nnf]) ).
cnf(c112,plain,
domain_of(inverse(x)) != range_of(x),
inference(cnf_transformation,[status(esa)],[f112_sk]) ).
cnf(u51,axiom,
eq(domain_of(inverse(x)),range_of(x)) = false,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(f37,axiom,
domain_of(flip(cross_product(Y,universal_class))) = inverse(Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f37_nnf,plain,
! [Y] : domain_of(flip(cross_product(Y,universal_class))) = inverse(Y),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [Y] : domain_of(flip(cross_product(Y,universal_class))) = inverse(Y),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(d5,axiom,
domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(f38,axiom,
domain_of(inverse(Z)) = range_of(Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f38_nnf,plain,
! [Z] : domain_of(inverse(Z)) = range_of(Z),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [Z] : domain_of(inverse(Z)) = range_of(Z),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
domain_of(inverse(X0)) = range_of(X0),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(u38,axiom,
domain_of(inverse(X0)) = range_of(X0),
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(d6,axiom,
domain_of(domain_of(flip(cross_product(X0,universal_class)))) = range_of(X0),
inference(definition_unfolding,[status(thm)],[u38,d5]) ).
cnf(t51,plain,
eq(domain_of(domain_of(flip(cross_product(x,universal_class)))),domain_of(domain_of(flip(cross_product(x,universal_class))))) = false,
inference(definition_unfolding,[status(thm)],[u51,d5,d6]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t118,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t429,plain,
true = false,
inference(step,[status(thm)],[t51,t118]) ).
cnf(t369,plain,
false = true,
inference(orient,[status(thm)],[t429]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/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/sandbox2/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c112]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t369]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET296-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n019.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 10:31:11 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/5.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.85 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------