%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:51:23 PM UTC 2026
% Result : Theorem 17.64s 3.03s
% Output : Proof 17.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 41 unt; 0 def)
% Number of atoms : 101 ( 60 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 66 ( 27 ~; 13 |; 19 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 28 ( 2 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f8_nnf,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
( one_to_one(sk1)
& function(sk1)
& relation(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f8_nnf]) ).
cnf(c13,plain,
one_to_one(sk1),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t3,plain,
one_to_one(sk1) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t874,plain,
one_to_one(sk1) = true,
inference(orient,[status(thm)],[t3]) ).
fof(f4,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f4_nnf,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(relation(X0),true,relation(relation_inverse(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f10,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f10_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [A] :
( ( relation_dom(A) != relation_rng(function_inverse(A))
| relation_rng(A) != relation_dom(function_inverse(A)) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ( relation_dom(sk2) != relation_rng(function_inverse(sk2))
| relation_rng(sk2) != relation_dom(function_inverse(sk2)) )
& one_to_one(sk2)
& function(sk2)
& relation(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f10_nnf]) ).
cnf(c16,plain,
relation(sk2),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi14,negated_conjecture,
relation(sk2) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h17,plain,
relation(relation_inverse(sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi14]) ).
cnf(h47,plain,
relation(relation_inverse(relation_inverse(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi3,h17]) ).
cnf(h93,plain,
relation(relation_inverse(relation_inverse(relation_inverse(sk2)))) = true,
inference(hyper_resolution,[status(thm)],[hi3,h47]) ).
fof(f9,axiom,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f9_nnf,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c14,plain,
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi12,axiom,
ifeq(relation(X0),true,relation_rng(X0),relation_dom(relation_inverse(X0))) = relation_dom(relation_inverse(X0)),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t191,plain,
relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sk2))))) = relation_rng(relation_inverse(relation_inverse(relation_inverse(sk2)))),
inference(hyper_resolution,[status(thm)],[hi12,h93]) ).
fof(f6,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f6_nnf,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c8,plain,
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(relation(X0),true,relation_inverse(relation_inverse(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t120,plain,
relation_inverse(relation_inverse(relation_inverse(relation_inverse(sk2)))) = relation_inverse(relation_inverse(sk2)),
inference(hyper_resolution,[status(thm)],[hi6,h47]) ).
cnf(t343,plain,
relation_inverse(relation_inverse(relation_inverse(relation_inverse(sk2)))) = relation_inverse(relation_inverse(sk2)),
inference(orient,[status(thm)],[t120]) ).
cnf(t953,plain,
relation_dom(relation_inverse(relation_inverse(sk2))) = relation_rng(relation_inverse(relation_inverse(relation_inverse(sk2)))),
inference(step,[status(thm)],[t191,t343]) ).
cnf(t21,plain,
relation_inverse(relation_inverse(sk2)) = sk2,
inference(hyper_resolution,[status(thm)],[hi6,hi14]) ).
cnf(t529,plain,
relation_inverse(relation_inverse(sk2)) = sk2,
inference(orient,[status(thm)],[t21]) ).
cnf(t954,plain,
relation_dom(sk2) = relation_rng(relation_inverse(relation_inverse(relation_inverse(sk2)))),
inference(step,[status(thm)],[t953,t529]) ).
cnf(t73,plain,
relation_inverse(relation_inverse(relation_inverse(sk2))) = relation_inverse(sk2),
inference(hyper_resolution,[status(thm)],[hi6,h17]) ).
cnf(t421,plain,
relation_inverse(relation_inverse(relation_inverse(sk2))) = relation_inverse(sk2),
inference(orient,[status(thm)],[t73]) ).
cnf(t955,plain,
relation_dom(sk2) = relation_rng(relation_inverse(sk2)),
inference(step,[status(thm)],[t954,t421]) ).
cnf(t913,plain,
relation_rng(relation_inverse(sk2)) = relation_dom(sk2),
inference(orient,[status(thm)],[t955]) ).
cnf(c15,plain,
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi13,axiom,
ifeq(relation(X0),true,relation_dom(X0),relation_rng(relation_inverse(X0))) = relation_rng(relation_inverse(X0)),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t207,plain,
relation_rng(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sk2))))) = relation_dom(relation_inverse(relation_inverse(relation_inverse(sk2)))),
inference(hyper_resolution,[status(thm)],[hi13,h93]) ).
cnf(t969,plain,
relation_rng(relation_inverse(relation_inverse(sk2))) = relation_dom(relation_inverse(relation_inverse(relation_inverse(sk2)))),
inference(step,[status(thm)],[t207,t343]) ).
cnf(t970,plain,
relation_rng(sk2) = relation_dom(relation_inverse(relation_inverse(relation_inverse(sk2)))),
inference(step,[status(thm)],[t969,t529]) ).
cnf(t971,plain,
relation_rng(sk2) = relation_dom(relation_inverse(sk2)),
inference(step,[status(thm)],[t970,t421]) ).
cnf(t919,plain,
relation_dom(relation_inverse(sk2)) = relation_rng(sk2),
inference(orient,[status(thm)],[t971]) ).
cnf(t51,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t51]) ).
cnf(c19,plain,
( relation_dom(sk2) != relation_rng(function_inverse(sk2))
| relation_rng(sk2) != relation_dom(function_inverse(sk2)) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != ifeq(relation_rng(sk2),relation_dom(relation_inverse(sk2)),ifeq(relation_dom(sk2),relation_rng(relation_inverse(sk2)),false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(relation_rng(sk2),relation_dom(relation_inverse(sk2)),ifeq(relation_dom(sk2),relation_rng(relation_inverse(sk2)),false,one_to_one(sk1)),true),
inference(rw,[status(thm)],[g0_0,t874]) ).
cnf(g0_2,plain,
true != ifeq(relation_rng(sk2),relation_dom(relation_inverse(sk2)),ifeq(relation_rng(relation_inverse(sk2)),relation_rng(relation_inverse(sk2)),false,one_to_one(sk1)),true),
inference(rw,[status(thm)],[g0_1,t913]) ).
cnf(g0_3,plain,
true != ifeq(relation_rng(sk2),relation_dom(relation_inverse(sk2)),ifeq(relation_rng(relation_inverse(sk2)),relation_dom(sk2),false,one_to_one(sk1)),true),
inference(rw,[status(thm)],[g0_2,t913]) ).
cnf(g0_4,plain,
true != ifeq(relation_rng(sk2),relation_rng(sk2),ifeq(relation_rng(relation_inverse(sk2)),relation_dom(sk2),false,one_to_one(sk1)),true),
inference(rw,[status(thm)],[g0_3,t919]) ).
cnf(g0_5,plain,
true != ifeq(relation_rng(relation_inverse(sk2)),relation_dom(sk2),false,one_to_one(sk1)),
inference(rw,[status(thm)],[g0_4,t256]) ).
cnf(g0_6,plain,
true != ifeq(relation_rng(relation_inverse(sk2)),relation_dom(sk2),false,true),
inference(rw,[status(thm)],[g0_5,t874]) ).
cnf(g0_7,plain,
true != ifeq(relation_dom(sk2),relation_dom(sk2),false,true),
inference(rw,[status(thm)],[g0_6,t913]) ).
cnf(g0_8,plain,
true != false,
inference(rw,[status(thm)],[g0_7,t256]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:14:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.64/3.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.64/3.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------