%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU010+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 02:50:50 PM UTC 2026
% Result : Theorem 12.59s 7.39s
% Output : Proof 12.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 26 unt; 0 def)
% Number of atoms : 102 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 105 ( 57 ~; 27 |; 14 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 66 ( 5 sgn 43 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_rng(B),A)
=> relation_composition(B,identity_relation(A)) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_relat_1) ).
fof(f37_nnf,plain,
! [A,B] :
( relation_composition(B,identity_relation(A)) = B
| ~ subset(relation_rng(B),A)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [B,A] :
( relation_composition(B,identity_relation(A)) = B
| ~ subset(relation_rng(B),A)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c55,plain,
( relation_composition(X1,identity_relation(X0)) = X1
| ~ subset(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi48,axiom,
ifeq(relation(X0),true,ifeq(subset(relation_rng(X0),X1),true,relation_composition(X0,identity_relation(X1)),X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c55]) ).
fof(f35,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( relation_composition(A,identity_relation(relation_rng(A))) = A
& relation_composition(identity_relation(relation_dom(A)),A) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_1) ).
fof(f35_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( relation_composition(A,identity_relation(relation_rng(A))) = A
& relation_composition(identity_relation(relation_dom(A)),A) = A ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [A] :
( ( relation_composition(A,identity_relation(relation_rng(A))) != A
| relation_composition(identity_relation(relation_dom(A)),A) != A )
& function(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ( relation_composition(sk9,identity_relation(relation_rng(sk9))) != sk9
| relation_composition(identity_relation(relation_dom(sk9)),sk9) != sk9 )
& function(sk9)
& relation(sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f35_nnf]) ).
cnf(c51,plain,
relation(sk9),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi45,negated_conjecture,
relation(sk9) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
fof(f21,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f21_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c28,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi24,axiom,
subset(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h127,plain,
relation_composition(sk9,identity_relation(relation_rng(sk9))) = sk9,
inference(hyper_resolution,[status(thm)],[hi48,hi45,hi24]) ).
fof(f36,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_dom(B),A)
=> relation_composition(identity_relation(A),B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_relat_1) ).
fof(f36_nnf,plain,
! [A,B] :
( relation_composition(identity_relation(A),B) = B
| ~ subset(relation_dom(B),A)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [B,A] :
( relation_composition(identity_relation(A),B) = B
| ~ subset(relation_dom(B),A)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c54,plain,
( relation_composition(identity_relation(X0),X1) = X1
| ~ subset(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi47,axiom,
ifeq(relation(X0),true,ifeq(subset(relation_dom(X0),X1),true,relation_composition(identity_relation(X1),X0),X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(h134,plain,
relation_composition(identity_relation(relation_dom(sk9)),sk9) = sk9,
inference(hyper_resolution,[status(thm)],[hi47,hi45,hi24]) ).
cnf(c53,plain,
( relation_composition(sk9,identity_relation(relation_rng(sk9))) != sk9
| relation_composition(identity_relation(relation_dom(sk9)),sk9) != sk9 ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi55,negated_conjecture,
ifeq(relation_composition(identity_relation(relation_dom(sk9)),sk9),sk9,ifeq(relation_composition(sk9,identity_relation(relation_rng(sk9))),sk9,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t3,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi55,h134,h127]) ).
cnf(t1293,plain,
false = true,
inference(orient,[status(thm)],[t3]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f6,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f6_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c9,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f9,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f9_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c12,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f19,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f19_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c26,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f30,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f30_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
( relation(sk5)
& ~ empty(sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f30_nnf]) ).
cnf(c43,plain,
~ empty(sk5),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f33,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f33_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
~ empty(sk8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f33_nnf]) ).
cnf(c48,plain,
~ empty(sk8),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c9,c12,c26,c43,c48,c53]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1293]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU010+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.64 % Computer : n008.cluster.edu
% 0.09/5.64 % Model : x86_64 x86_64
% 0.09/5.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.64 % Memory : 8046.5625MB
% 0.09/5.64 % OS : Linux 6.8.0-71-generic
% 0.09/5.64 % CPULimit : 300
% 0.09/5.64 % WCLimit : 300
% 0.09/5.64 % DateTime : Thu Sep 24 12:34:30 UTC 2026
% 0.09/5.64 % CPUTime :
% 0.09/5.64 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.59/7.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.59/7.39 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------