%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:11:58 PM UTC 2026
% Result : Unsatisfiable 5.46s 1.61s
% Output : Proof 5.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 45 unt; 0 def)
% Number of atoms : 121 ( 44 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 115 ( 62 ~; 30 |; 18 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 75 ( 2 sgn 47 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X,A,B] :
( in_lopen(X,A,B)
<=> ( leq(X,B)
& less(A,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_lopen) ).
fof(f10_nnf,plain,
! [X,A,B] :
( ( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) )
& ( ( leq(X,B)
& less(A,X) )
| ~ in_lopen(X,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,A,B] :
( ( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) )
& ( ( leq(X,B)
& less(A,X) )
| ~ in_lopen(X,A,B) ) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c15,plain,
( leq(X0,X2)
| ~ in_lopen(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi14,axiom,
ifeq(in_lopen(X0,X1,X2),true,leq(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
fof(f34,axiom,
in_lopen(w,v0,v600),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wit_in_lopen) ).
fof(f34_nnf,plain,
in_lopen(w,v0,v600),
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c54,plain,
in_lopen(w,v0,v600),
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(hi46,axiom,
in_lopen(w,v0,v600) = true,
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(h102,plain,
leq(w,v600) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi46]) ).
fof(f8,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox/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]) ).
fof(f35,axiom,
leq(v800,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wit_leq) ).
fof(f35_nnf,plain,
leq(v800,w),
inference(nnf_transformation,[status(thm)],[f35]) ).
cnf(c55,plain,
leq(v800,w),
inference(cnf_transformation,[status(esa)],[f35_nnf]) ).
cnf(hi47,axiom,
leq(v800,w) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(h114,plain,
leq(v800,v600) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi47,h102]) ).
fof(f5,axiom,
! [X,Y] :
( less(X,Y)
=> leq(X,Y) ),
file('/export/starexec/sandbox/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(f31,axiom,
less(v600,v800),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v600_v800) ).
fof(f31_nnf,plain,
less(v600,v800),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c49,plain,
less(v600,v800),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi44,axiom,
less(v600,v800) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(h34,plain,
leq(v600,v800) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi44]) ).
fof(f4,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
=> X = Y ),
file('/export/starexec/sandbox/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(h147,plain,
v600 = v800,
inference(hyper_resolution,[status(thm)],[hi5,h34,h114]) ).
fof(f32,axiom,
( v600 != v800
& v0 != v800
& v0 != v600 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct) ).
fof(f32_nnf,plain,
( v600 != v800
& v0 != v800
& v0 != v600 ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
( v600 != v800
& v0 != v800
& v0 != v600 ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c52,plain,
v600 != v800,
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(hi55,axiom,
ifeq(v600,v800,false,true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi55,h147]) ).
cnf(t1643,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f0,axiom,
! [X] : ~ less(X,X),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(c50,plain,
v0 != v600,
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(c51,plain,
v0 != v800,
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c23,c35,c36,c37,c50,c51,c52]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1643]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 01:25:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.46/1.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.46/1.61 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------