%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% 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 02:52:00 PM UTC 2026
% Result : Theorem 20.04s 2.99s
% Output : Proof 20.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 33 unt; 0 def)
% Number of atoms : 164 ( 19 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 175 ( 72 ~; 50 |; 34 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 87 ( 2 sgn 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] :
( ( l1_orders_2(B)
& l1_orders_2(A) )
=> ( l1_orders_2(k1_latsum_1(A,B))
& v1_orders_2(k1_latsum_1(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(f7_nnf,plain,
! [A,B] :
( ( l1_orders_2(k1_latsum_1(A,B))
& v1_orders_2(k1_latsum_1(A,B)) )
| ~ l1_orders_2(B)
| ~ l1_orders_2(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ( l1_orders_2(k1_latsum_1(A,B))
& v1_orders_2(k1_latsum_1(A,B)) )
| ~ l1_orders_2(B)
| ~ l1_orders_2(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c18,plain,
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi16,axiom,
ifeq(l1_orders_2(X0),true,ifeq(l1_orders_2(X1),true,l1_orders_2(k1_latsum_1(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
fof(f0,conjecture,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_latsum_1) ).
fof(f0_neg,negated_conjecture,
~ ! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ r2_hidden(C,u1_struct_0(A))
& r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B))) )
& m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) )
& l1_orders_2(B) )
& l1_orders_2(A) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( ~ r2_hidden(sk2,u1_struct_0(sk0))
& r2_hidden(sk3,u1_struct_0(sk0))
& r1_orders_2(k1_latsum_1(sk0,sk1),sk2,sk3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sk0),u1_struct_0(sk1)),k1_zfmisc_1(u1_struct_0(sk1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sk0),u1_struct_0(sk1)),sk1)
& m1_subset_1(sk3,u1_struct_0(k1_latsum_1(sk0,sk1)))
& m1_subset_1(sk2,u1_struct_0(k1_latsum_1(sk0,sk1)))
& l1_orders_2(sk1)
& l1_orders_2(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f0_nnf]) ).
cnf(c0,plain,
l1_orders_2(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
l1_orders_2(sk0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c1,plain,
l1_orders_2(sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
l1_orders_2(sk1) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h7,plain,
l1_orders_2(k1_latsum_1(sk0,sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi16,hi0,hi1]) ).
fof(f5,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f5_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ r2_hidden(k4_tarski(B,C),u1_orders_2(A))
| r1_orders_2(A,B,C) )
& ( r2_hidden(k4_tarski(B,C),u1_orders_2(A))
| ~ r1_orders_2(A,B,C) ) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l1_orders_2(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ( ( ~ r2_hidden(k4_tarski(B,C),u1_orders_2(A))
| r1_orders_2(A,B,C) )
& ( r2_hidden(k4_tarski(B,C),u1_orders_2(A))
| ~ r1_orders_2(A,B,C) ) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_orders_2(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c13,plain,
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi11,axiom,
ifeq(l1_orders_2(X0),true,ifeq(m1_subset_1(X1,u1_struct_0(X0)),true,ifeq(m1_subset_1(X2,u1_struct_0(X0)),true,ifeq(r1_orders_2(X0,X1,X2),true,r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c2,plain,
m1_subset_1(sk2,u1_struct_0(k1_latsum_1(sk0,sk1))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
m1_subset_1(sk2,u1_struct_0(k1_latsum_1(sk0,sk1))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c3,plain,
m1_subset_1(sk3,u1_struct_0(k1_latsum_1(sk0,sk1))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi3,negated_conjecture,
m1_subset_1(sk3,u1_struct_0(k1_latsum_1(sk0,sk1))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(c6,plain,
r1_orders_2(k1_latsum_1(sk0,sk1),sk2,sk3),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi6,negated_conjecture,
r1_orders_2(k1_latsum_1(sk0,sk1),sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h230,plain,
r2_hidden(k4_tarski(sk2,sk3),u1_orders_2(k1_latsum_1(sk0,sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h7,hi2,hi3,hi6]) ).
fof(f33,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C,D] :
( ( r2_hidden(D,u1_struct_0(A))
& r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_latsum_1) ).
fof(f33_nnf,plain,
! [A] :
( ! [B] :
( ! [C,D] :
( r2_hidden(C,u1_struct_0(A))
| ~ r2_hidden(D,u1_struct_0(A))
| ~ r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
| ~ l1_orders_2(B) )
| ~ l1_orders_2(A) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [A,B,C,D] :
( r2_hidden(C,u1_struct_0(A))
| ~ r2_hidden(D,u1_struct_0(A))
| ~ r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
| ~ l1_orders_2(B)
| ~ l1_orders_2(A) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c46,plain,
( r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(hi34,axiom,
ifeq(l1_orders_2(X0),true,ifeq(l1_orders_2(X1),true,ifeq(v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1),true,ifeq(m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1))),true,ifeq(r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1))),true,ifeq(r2_hidden(X3,u1_struct_0(X0)),true,r2_hidden(X2,u1_struct_0(X0)),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(c4,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sk0),u1_struct_0(sk1)),sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi4,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(sk0),u1_struct_0(sk1)),sk1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c5,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sk0),u1_struct_0(sk1)),k1_zfmisc_1(u1_struct_0(sk1))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi5,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(sk0),u1_struct_0(sk1)),k1_zfmisc_1(u1_struct_0(sk1))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(c7,plain,
r2_hidden(sk3,u1_struct_0(sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi7,negated_conjecture,
r2_hidden(sk3,u1_struct_0(sk0)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h5672,plain,
r2_hidden(sk2,u1_struct_0(sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi34,hi0,hi1,hi4,hi5,h230,hi7]) ).
cnf(c8,plain,
~ r2_hidden(sk2,u1_struct_0(sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(r2_hidden(sk2,u1_struct_0(sk0)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi42,h5672]) ).
cnf(t266,plain,
false = true,
inference(orient,[status(thm)],[t1]) ).
fof(f2,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2_nnf,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c10,plain,
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f29,axiom,
? [A] : ~ v1_xboole_0(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f29_nnf,plain,
? [A] : ~ v1_xboole_0(A),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
~ v1_xboole_0(sk10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f29_nnf]) ).
cnf(c41,plain,
~ v1_xboole_0(sk10),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f38,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f38_nnf,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c52,plain,
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f40,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f40_nnf,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c54,plain,
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c8,c10,c41,c52,c54]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t266]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n008.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 14:05:10 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.04/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.04/2.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------