%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU040+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 02:50:52 PM UTC 2026
% Result : Theorem 3.95s 2.15s
% Output : Proof 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 21 unt; 0 def)
% Number of atoms : 89 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 51 ~; 21 |; 14 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 64 ( 9 sgn 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
fof(f37_nnf,plain,
! [A,B] :
( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [B,A] :
( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c59,plain,
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi50,axiom,
ifeq(relation(X0),true,subset(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
fof(f35,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
& subset(relation_dom(relation_dom_restriction(B,A)),relation_dom(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_1) ).
fof(f35_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
& subset(relation_dom(relation_dom_restriction(B,A)),relation_dom(B)) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [A,B] :
( ( ~ subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ subset(relation_dom(relation_dom_restriction(B,A)),relation_dom(B)) )
& function(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ( ~ subset(relation_rng(relation_dom_restriction(sk12,sk11)),relation_rng(sk12))
| ~ subset(relation_dom(relation_dom_restriction(sk12,sk11)),relation_dom(sk12)) )
& function(sk12)
& relation(sk12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12])],[f35_nnf]) ).
cnf(c55,plain,
relation(sk12),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi47,negated_conjecture,
relation(sk12) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(h53,plain,
subset(relation_rng(relation_dom_restriction(sk12,V0)),relation_rng(sk12)) = true,
inference(hyper_resolution,[status(thm)],[hi50,hi47]) ).
fof(f36,axiom,
! [A,B] :
( relation(B)
=> subset(relation_dom(relation_dom_restriction(B,A)),relation_dom(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_relat_1) ).
fof(f36_nnf,plain,
! [A,B] :
( subset(relation_dom(relation_dom_restriction(B,A)),relation_dom(B))
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [B,A] :
( subset(relation_dom(relation_dom_restriction(B,A)),relation_dom(B))
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c58,plain,
( subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi49,axiom,
ifeq(relation(X0),true,subset(relation_dom(relation_dom_restriction(X0,X1)),relation_dom(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(h54,plain,
subset(relation_dom(relation_dom_restriction(sk12,V0)),relation_dom(sk12)) = true,
inference(hyper_resolution,[status(thm)],[hi49,hi47]) ).
cnf(c57,plain,
( ~ subset(relation_rng(relation_dom_restriction(sk12,sk11)),relation_rng(sk12))
| ~ subset(relation_dom(relation_dom_restriction(sk12,sk11)),relation_dom(sk12)) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi57,negated_conjecture,
ifeq(subset(relation_dom(relation_dom_restriction(sk12,sk11)),relation_dom(sk12)),true,ifeq(subset(relation_rng(relation_dom_restriction(sk12,sk11)),relation_rng(sk12)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(t6,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi57,h54,h53]) ).
cnf(t1055,plain,
false = true,
inference(orient,[status(thm)],[t6]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/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/sandbox/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(f11,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f11_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c16,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f20,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f20_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c28,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f30,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/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(sk7)
& ~ empty(sk7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f30_nnf]) ).
cnf(c47,plain,
~ empty(sk7),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f33,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f33_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
~ empty(sk10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f33_nnf]) ).
cnf(c52,plain,
~ empty(sk10),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c9,c16,c28,c47,c52,c57]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1055]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU040+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:38:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.95/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/2.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------