%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT082+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 02:11:56 PM UTC 2026
% Result : Theorem 13.04s 2.15s
% Output : Proof 13.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 89 ( 61 unt; 0 def)
% Number of atoms : 217 ( 118 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 266 ( 138 ~; 31 |; 92 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 15 con; 0-4 aty)
% Number of variables : 90 ( 4 sgn 47 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(X,B)
& leq(A,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_closed) ).
fof(f9_nnf,plain,
! [X,A,B] :
( ( ~ leq(X,B)
| ~ leq(A,X)
| in_closed(X,A,B) )
& ( ( leq(X,B)
& leq(A,X) )
| ~ in_closed(X,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,A,B] :
( ( ~ leq(X,B)
| ~ leq(A,X)
| in_closed(X,A,B) )
& ( ( leq(X,B)
& leq(A,X) )
| ~ in_closed(X,A,B) ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c12,plain,
( leq(X0,X2)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi11,axiom,
ifeq(in_closed(X0,X1,X2),true,leq(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f56,conjecture,
~ ? [X,Y,Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& in_open(Y,v0,v500)
& less(v300,Y)
& in_closed(X,v601,v601)
& in_closed(X,v600,v600) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odrl411) ).
fof(f56_neg,negated_conjecture,
~ ~ ? [X,Y,Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& in_open(Y,v0,v500)
& less(v300,Y)
& in_closed(X,v601,v601)
& in_closed(X,v600,v600) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f56_nnf,plain,
? [X,Y,Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& in_open(Y,v0,v500)
& less(v300,Y)
& in_closed(X,v601,v601)
& in_closed(X,v600,v600) ),
inference(nnf_transformation,[status(thm)],[f56_neg]) ).
fof(f56_sk,plain,
( in_lopen(sk5,v0,v32)
& leq(v16,sk5)
& in_open(sk4,v0,v500)
& less(v300,sk4)
& in_closed(sk3,v601,v601)
& in_closed(sk3,v600,v600) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f56_nnf]) ).
cnf(c94,plain,
in_closed(sk3,v600,v600),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(hi68,negated_conjecture,
in_closed(sk3,v600,v600) = true,
inference(equality_encoding,[status(esa)],[c94]) ).
cnf(h143,plain,
leq(sk3,v600) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi68]) ).
cnf(c11,plain,
( leq(X1,X0)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi10,axiom,
ifeq(in_closed(X0,X1,X2),true,leq(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(c95,plain,
in_closed(sk3,v601,v601),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(hi69,negated_conjecture,
in_closed(sk3,v601,v601) = true,
inference(equality_encoding,[status(esa)],[c95]) ).
cnf(h151,plain,
leq(v601,sk3) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi69]) ).
fof(f8,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_trans) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi9,axiom,
ifeq(leq(X0,X1),true,ifeq(leq(X1,X2),true,leq(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h2163,plain,
leq(v601,v600) = true,
inference(hyper_resolution,[status(thm)],[hi9,h151,h143]) ).
fof(f5,axiom,
! [X,Y] :
( less(X,Y)
=> leq(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_implies_leq) ).
fof(f5_nnf,plain,
! [X,Y] :
( leq(X,Y)
| ~ less(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( leq(X,Y)
| ~ less(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( leq(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi6,axiom,
ifeq(less(X0,X1),true,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f54,axiom,
less(v600,v601),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v600_v601) ).
fof(f54_nnf,plain,
less(v600,v601),
inference(nnf_transformation,[status(thm)],[f54]) ).
cnf(c72,plain,
less(v600,v601),
inference(cnf_transformation,[status(esa)],[f54_nnf]) ).
cnf(hi67,axiom,
less(v600,v601) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(h139,plain,
leq(v600,v601) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi67]) ).
fof(f4,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
=> X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_antisym) ).
fof(f4_nnf,plain,
! [X,Y] :
( X = Y
| ~ leq(Y,X)
| ~ leq(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( X = Y
| ~ leq(Y,X)
| ~ leq(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c6,plain,
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi5,axiom,
ifeq(leq(X0,X1),true,ifeq(leq(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h5075,plain,
v600 = v601,
inference(hyper_resolution,[status(thm)],[hi5,h139,h2163]) ).
fof(f55,axiom,
( v600 != v601
& v500 != v601
& v500 != v600
& v300 != v601
& v300 != v600
& v300 != v500
& v32 != v601
& v32 != v600
& v32 != v500
& v32 != v300
& v16 != v601
& v16 != v600
& v16 != v500
& v16 != v300
& v16 != v32
& v0 != v601
& v0 != v600
& v0 != v500
& v0 != v300
& v0 != v32
& v0 != v16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct) ).
fof(f55_nnf,plain,
( v600 != v601
& v500 != v601
& v500 != v600
& v300 != v601
& v300 != v600
& v300 != v500
& v32 != v601
& v32 != v600
& v32 != v500
& v32 != v300
& v16 != v601
& v16 != v600
& v16 != v500
& v16 != v300
& v16 != v32
& v0 != v601
& v0 != v600
& v0 != v500
& v0 != v300
& v0 != v32
& v0 != v16 ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
( v600 != v601
& v500 != v601
& v500 != v600
& v300 != v601
& v300 != v600
& v300 != v500
& v32 != v601
& v32 != v600
& v32 != v500
& v32 != v300
& v16 != v601
& v16 != v600
& v16 != v500
& v16 != v300
& v16 != v32
& v0 != v601
& v0 != v600
& v0 != v500
& v0 != v300
& v0 != v32
& v0 != v16 ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c93,plain,
v600 != v601,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(hi99,axiom,
ifeq(v600,v601,false,true) = true,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi99,h5075]) ).
cnf(t1004,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f0,axiom,
! [X] : ~ less(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive) ).
fof(f0_nnf,plain,
! [X] : ~ less(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ less(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ less(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f13,axiom,
! [I1lo,I1hi,I2lo,I2hi] :
( axis_conflict(I1lo,I1hi,I2lo,I2hi)
<=> ~ ? [X] :
( in_closed(X,I2lo,I2hi)
& in_closed(X,I1lo,I1hi) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axis_conflict_def) ).
fof(f13_nnf,plain,
! [I1lo,I1hi,I2lo,I2hi] :
( ( ? [X] :
( in_closed(X,I2lo,I2hi)
& in_closed(X,I1lo,I1hi) )
| axis_conflict(I1lo,I1hi,I2lo,I2hi) )
& ( ! [X] :
( ~ in_closed(X,I2lo,I2hi)
| ~ in_closed(X,I1lo,I1hi) )
| ~ axis_conflict(I1lo,I1hi,I2lo,I2hi) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [I1lo,I1hi,I2lo,I2hi,X] :
( ( ( in_closed(sk0(I1lo,I1hi,I2lo,I2hi),I2lo,I2hi)
& in_closed(sk0(I1lo,I1hi,I2lo,I2hi),I1lo,I1hi) )
| axis_conflict(I1lo,I1hi,I2lo,I2hi) )
& ( ~ in_closed(X,I2lo,I2hi)
| ~ in_closed(X,I1lo,I1hi)
| ~ axis_conflict(I1lo,I1hi,I2lo,I2hi) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f13_nnf]) ).
cnf(c23,plain,
( ~ in_closed(X4,X2,X3)
| ~ in_closed(X4,X0,X1)
| ~ axis_conflict(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f19,axiom,
conflict != compatible,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verdicts_distinct_cf_cp) ).
fof(f19_nnf,plain,
conflict != compatible,
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
conflict != compatible,
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c35,plain,
conflict != compatible,
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f20,axiom,
conflict != unknown,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verdicts_distinct_cf_un) ).
fof(f20_nnf,plain,
conflict != unknown,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
conflict != unknown,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c36,plain,
conflict != unknown,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f21,axiom,
compatible != unknown,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verdicts_distinct_cp_un) ).
fof(f21_nnf,plain,
compatible != unknown,
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
compatible != unknown,
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c37,plain,
compatible != unknown,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(c73,plain,
v0 != v16,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c74,plain,
v0 != v32,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c75,plain,
v0 != v300,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c76,plain,
v0 != v500,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c77,plain,
v0 != v600,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c78,plain,
v0 != v601,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c79,plain,
v16 != v32,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c80,plain,
v16 != v300,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c81,plain,
v16 != v500,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c82,plain,
v16 != v600,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c83,plain,
v16 != v601,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c84,plain,
v32 != v300,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c85,plain,
v32 != v500,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c86,plain,
v32 != v600,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c87,plain,
v32 != v601,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c88,plain,
v300 != v500,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c89,plain,
v300 != v600,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c90,plain,
v300 != v601,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c91,plain,
v500 != v600,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(c92,plain,
v500 != v601,
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c23,c35,c36,c37,c73,c74,c75,c76,c77,c78,c79,c80,c81,c82,c83,c84,c85,c86,c87,c88,c89,c90,c91,c92,c93]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1004]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT082+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 01:27:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.04/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.04/2.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------