TSTP Solution File: AGT029^1 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : AGT029^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 03:39:36 EDT 2024
% Result : Theorem 84.97s 20.40s
% Output : Refutation 85.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 116
% Syntax : Number of formulae : 417 ( 64 unt; 41 typ; 8 def)
% Number of atoms : 1560 ( 122 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 4699 ( 783 ~; 556 |; 0 &;3360 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 331 ( 331 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 12 con; 0-3 aty)
% Number of variables : 1137 ( 315 ^ 821 !; 1 ?;1137 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: $i > $o,B: $i] :
~ ( A @ B ) ) ) ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mforall_ind_def,definition,
( mforall_ind
= ( ^ [A: mu > $i > $o,B: $i] :
! [C: mu] : ( A @ C @ B ) ) ) ).
thf(mforall_prop_type,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(mforall_prop_def,definition,
( mforall_prop
= ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
! [C: $i > $o] : ( A @ C @ B ) ) ) ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mexists_ind_def,definition,
( mexists_ind
= ( ^ [A: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [B: mu] : ( mnot @ ( A @ B ) ) ) ) ) ) ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
! [D: $i] :
( ~ ( A @ C @ D )
| ( B @ D ) ) ) ) ).
thf(mdia_type,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(r1_type,type,
r1: $i > $i > $o ).
thf(r2_type,type,
r2: $i > $i > $o ).
thf(r3_type,type,
r3: $i > $i > $o ).
thf(r4_type,type,
r4: $i > $i > $o ).
thf(r5_type,type,
r5: $i > $i > $o ).
thf(john_type,type,
john: mu ).
thf(tom_type,type,
tom: mu ).
thf(peter_type,type,
peter: mu ).
thf(mike_type,type,
mike: mu ).
thf(good_in_maths_type,type,
good_in_maths: mu > $i > $o ).
thf(maths_teacher_type,type,
maths_teacher: mu > $i > $o ).
thf(mathematician_type,type,
mathematician: mu > $i > $o ).
thf(maths_student_type,type,
maths_student: mu > $i > $o ).
thf(good_in_physics_type,type,
good_in_physics: mu > $i > $o ).
thf(physics_student_type,type,
physics_student: mu > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: mu > $i ).
thf(sk3_type,type,
sk3: $i > mu > $i > $i ).
thf(sk4_type,type,
sk4: ( $i > $o ) > $i > $i ).
thf(sk5_type,type,
sk5: ( $i > $o ) > $i > $i ).
thf(sk6_type,type,
sk6: ( $i > $o ) > $i > $i ).
thf(sk7_type,type,
sk7: ( $i > $o ) > $i > $i ).
thf(sk8_type,type,
sk8: ( $i > $o ) > $i > $i ).
thf(sk9_type,type,
sk9: $i > ( $i > $o ) > $i > $i ).
thf(sk10_type,type,
sk10: ( $i > $o ) > $i > $i ).
thf(sk11_type,type,
sk11: ( $i > $o ) > $i > $i ).
thf(sk12_type,type,
sk12: ( $i > $o ) > $i > $i ).
thf(sk13_type,type,
sk13: $i > mu > $i > $i ).
thf(sk14_type,type,
sk14: $i > mu > $i > $i ).
thf(sk15_type,type,
sk15: ( $i > $o ) > $i > $i ).
thf(sk16_type,type,
sk16: ( $i > $o ) > $i > $i ).
thf(sk19_type,type,
sk19: ( $i > $o ) > $i > $i ).
thf(18,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mnot @ ( mbox @ r4 @ ( mnot @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r4) ).
thf(120,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(122,plain,
! [B: $i > $o,A: $i] :
( ( r4 @ A @ ( sk19 @ B @ A ) )
| ( B @ ( sk20 @ B @ A ) ) ),
inference(cnf,[status(esa)],[120]) ).
thf(20582,plain,
! [A: $i] :
( ( r4 @ A
@ ( sk19
@ ^ [B: $i] : $false
@ A ) )
| $false ),
inference(prim_subst,[status(thm)],[122:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : $false ))]]) ).
thf(20769,plain,
! [A: $i] :
( r4 @ A
@ ( sk19
@ ^ [B: $i] : $false
@ A ) ),
inference(simp,[status(thm)],[20582]) ).
thf(1,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( mbox @ r2 @ ( good_in_maths @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( mbox @ r2 @ ( good_in_maths @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i] :
~ ! [B: mu] :
~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( good_in_maths @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
~ ~ ~ ! [A: $i] :
? [B: mu] :
! [C: $i] :
( ~ ( r2 @ A @ C )
| ( good_in_maths @ B @ C ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(72,plain,
! [A: mu] : ( r2 @ sk1 @ ( sk2 @ A ) ),
inference(cnf,[status(esa)],[70]) ).
thf(6,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mbox @ r2 @ ( mbox @ r4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r2) ).
thf(84,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ! [D: $i] :
( ~ ( r4 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(85,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( r4 @ A @ ( sk7 @ B @ A ) )
| ~ ( r2 @ A @ C )
| ~ ( r4 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[84]) ).
thf(2255,plain,
! [E: $i,D: $i,C: $i > $o,B: $i,A: mu] :
( ( r4 @ B @ ( sk7 @ C @ B ) )
| ~ ( r4 @ D @ E )
| ( C @ E )
| ( ( r2 @ sk1 @ ( sk2 @ A ) )
!= ( r2 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,85]) ).
thf(2256,plain,
! [C: mu,B: $i,A: $i > $o] :
( ( r4 @ sk1 @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( A @ B ) ),
inference(pattern_uni,[status(thm)],[2255:[bind(A,$thf( F )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk2 @ F ))]]) ).
thf(2439,plain,
! [C: mu,B: $i,A: $i > $o] :
( ( r4 @ sk1 @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( A @ B ) ),
inference(simp,[status(thm)],[2256]) ).
thf(2564,plain,
! [B: mu,A: $i] :
( ( r4 @ sk1
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
| ~ ( r4 @ ( sk2 @ B ) @ A )
| $false ),
inference(prim_subst,[status(thm)],[2439:[bind(A,$thf( ^ [D: $i] : $false ))]]) ).
thf(2659,plain,
! [B: mu,A: $i] :
( ( r4 @ sk1
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
| ~ ( r4 @ ( sk2 @ B ) @ A ) ),
inference(simp,[status(thm)],[2564]) ).
thf(21224,plain,
! [C: mu,B: $i,A: $i] :
( ( r4 @ sk1
@ ( sk7
@ ^ [D: $i] : $false
@ sk1 ) )
| ( ( r4 @ A
@ ( sk19
@ ^ [D: $i] : $false
@ A ) )
!= ( r4 @ ( sk2 @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20769,2659]) ).
thf(21225,plain,
( r4 @ sk1
@ ( sk7
@ ^ [A: $i] : $false
@ sk1 ) ),
inference(pattern_uni,[status(thm)],[21224:[bind(A,$thf( sk2 @ G )),bind(B,$thf( sk19 @ ^ [E: $i] : $false @ ( sk2 @ G ) )),bind(C,$thf( G ))]]) ).
thf(14,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r4 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r5_r4) ).
thf(108,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(109,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( r5 @ A @ ( sk15 @ B @ A ) )
| ~ ( r4 @ A @ C )
| ( B @ C ) ),
inference(cnf,[status(esa)],[108]) ).
thf(28987,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( r5 @ A @ ( sk15 @ B @ A ) )
| ( B @ C )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [D: $i] : $false
@ sk1 ) )
!= ( r4 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21225,109]) ).
thf(28988,plain,
! [A: $i > $o] :
( ( r5 @ sk1 @ ( sk15 @ A @ sk1 ) )
| ( A
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[28987:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk7 @ ^ [D: $i] : $false @ sk1 ))]]) ).
thf(29611,plain,
! [A: $i > $o] :
( ( r5 @ sk1 @ ( sk15 @ A @ sk1 ) )
| ( A
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ),
inference(simp,[status(thm)],[28988]) ).
thf(29963,plain,
( ( r5 @ sk1
@ ( sk15
@ ^ [A: $i] : $false
@ sk1 ) )
| $false ),
inference(prim_subst,[status(thm)],[29611:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(30296,plain,
( r5 @ sk1
@ ( sk15
@ ^ [A: $i] : $false
@ sk1 ) ),
inference(simp,[status(thm)],[29963]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk7 @ B @ A ) )
| ~ ( r2 @ A @ C )
| ~ ( r4 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[84]) ).
thf(2938,plain,
! [E: $i,D: $i,C: $i > $o,B: $i,A: mu] :
( ~ ( C @ ( sk7 @ C @ B ) )
| ~ ( r4 @ D @ E )
| ( C @ E )
| ( ( r2 @ sk1 @ ( sk2 @ A ) )
!= ( r2 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,86]) ).
thf(2939,plain,
! [C: mu,B: $i,A: $i > $o] :
( ~ ( A @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( A @ B ) ),
inference(pattern_uni,[status(thm)],[2938:[bind(A,$thf( F )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk2 @ F ))]]) ).
thf(3144,plain,
! [C: mu,B: $i,A: $i > $o] :
( ~ ( A @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( A @ B ) ),
inference(simp,[status(thm)],[2939]) ).
thf(3808,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ~ ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
| ~ ( r4 @ ( sk2 @ B ) @ A )
| ~ ( C @ A ) ),
inference(prim_subst,[status(thm)],[3144:[bind(A,$thf( ^ [E: $i] : ~ ( D @ E ) ))]]) ).
thf(4086,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( C @ A )
| ~ ( r4 @ ( sk2 @ B ) @ A )
| ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) ) ),
inference(cnf,[status(esa)],[3808]) ).
thf(4087,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( C @ A )
| ~ ( r4 @ ( sk2 @ B ) @ A )
| ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) ) ),
inference(simp,[status(thm)],[4086]) ).
thf(6092,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( C @ A )
| ~ ( r4 @ ( sk2 @ B ) @ A )
| ( ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
!= ( ~ ( C @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4087]) ).
thf(6182,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( C @ A )
| ~ ( r4 @ ( sk2 @ B ) @ A )
| ( ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
!= ( ~ ( C @ A ) ) ) ),
inference(simp,[status(thm)],[6092]) ).
thf(31518,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( r4 @ ( sk2 @ B ) @ A )
| ( ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
!= ( ~ ( C @ A ) ) )
| ( ( r5 @ sk1
@ ( sk15
@ ^ [D: $i] : $false
@ sk1 ) )
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30296,6182]) ).
thf(31672,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( r5 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r5 @ sk1 @ B )
@ sk1 ) )
!= ( ~ ( r5 @ sk1
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(pre_uni,[status(thm)],[31518:[bind(A,$thf( sk15 @ ^ [D: $i] : $false @ sk1 )),bind(B,$thf( B )),bind(C,$thf( r5 @ sk1 ))]]) ).
thf(31717,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( r5 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r5 @ sk1 @ B )
@ sk1 ) )
!= ( ~ ( r5 @ sk1
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[31672]) ).
thf(32157,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( r5 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r5 @ sk1 @ B )
@ sk1 ) )
!= ~ $true ) ),
inference(rewrite,[status(thm)],[31717,30296]) ).
thf(32158,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) )
| ( r5 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r5 @ sk1 @ B )
@ sk1 ) ) ),
inference(simp,[status(thm)],[32157]) ).
thf(23,axiom,
mvalid @ ( mbox @ r2 @ ( mathematician @ tom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a7) ).
thf(137,plain,
! [A: $i,B: $i] :
( ~ ( r2 @ A @ B )
| ( mathematician @ tom @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( r2 @ A @ B )
| ( mathematician @ tom @ B ) ),
inference(cnf,[status(esa)],[137]) ).
thf(11,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r3 @ ( mbox @ r5 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r3) ).
thf(99,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r3 @ A @ C )
| ! [D: $i] :
( ~ ( r5 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk12 @ B @ A ) )
| ~ ( r3 @ A @ C )
| ~ ( r5 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[99]) ).
thf(21279,plain,
! [D: mu,C: $i,B: $i > $o,A: $i] :
( ( r4 @ sk1 @ ( sk7 @ B @ sk1 ) )
| ( B @ C )
| ( ( r4 @ A
@ ( sk19
@ ^ [E: $i] : $false
@ A ) )
!= ( r4 @ ( sk2 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20769,2439]) ).
thf(21280,plain,
! [B: mu,A: $i > $o] :
( ( r4 @ sk1 @ ( sk7 @ A @ sk1 ) )
| ( A
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[21279:[bind(A,$thf( sk2 @ H )),bind(B,$thf( B )),bind(C,$thf( sk19 @ ^ [F: $i] : $false @ ( sk2 @ H ) )),bind(D,$thf( H ))]]) ).
thf(21450,plain,
! [B: mu,A: $i > $o] :
( ( r4 @ sk1 @ ( sk7 @ A @ sk1 ) )
| ( A
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) ) ),
inference(simp,[status(thm)],[21280]) ).
thf(124,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk19 @ B @ A ) )
| ( B @ ( sk20 @ B @ A ) ) ),
inference(cnf,[status(esa)],[120]) ).
thf(738,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk19 @ B @ A ) )
| ( ( B @ ( sk20 @ B @ A ) )
!= ( ~ ( B @ ( sk19 @ B @ A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[124]) ).
thf(777,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk19 @ B @ A ) )
| ( ( B @ ( sk20 @ B @ A ) )
!= ( ~ ( B @ ( sk19 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[738]) ).
thf(6064,plain,
! [D: $i > $o,C: mu,B: $i,A: mu] :
( ~ ( r4 @ ( sk2 @ C ) @ B )
| ( D
@ ( sk7
@ ^ [E: $i] :
~ ( D @ E )
@ sk1 ) )
| ( ( r2 @ sk1 @ ( sk2 @ A ) )
!= ( D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[72,4087]) ).
thf(6185,plain,
! [B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ( r2 @ sk1
@ ( sk7
@ ^ [C: $i] :
~ ( r2 @ sk1 @ C )
@ sk1 ) ) ),
inference(pre_uni,[status(thm)],[6064:[bind(A,$thf( A )),bind(B,$thf( sk2 @ A )),bind(C,$thf( C )),bind(D,$thf( r2 @ sk1 ))]]) ).
thf(6377,plain,
! [B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ( r2 @ sk1
@ ( sk7
@ ^ [C: $i] :
~ ( r2 @ sk1 @ C )
@ sk1 ) ) ),
inference(simp,[status(thm)],[6185]) ).
thf(3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r2 @ ( mimplies @ ( good_in_physics @ A ) @ ( mdia @ r2 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r5) ).
thf(73,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r2 @ A @ C )
| ~ ( good_in_physics @ B @ C )
| ~ ! [D: $i] :
( ~ ( r2 @ C @ D )
| ~ ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(74,plain,
! [C: $i,B: mu,A: $i] :
( ~ ( r2 @ A @ C )
| ~ ( good_in_physics @ B @ C )
| ( good_in_maths @ B @ ( sk3 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(71,plain,
! [A: mu] :
~ ( good_in_maths @ A @ ( sk2 @ A ) ),
inference(cnf,[status(esa)],[70]) ).
thf(456,plain,
! [D: mu,C: $i,B: mu,A: $i] :
( ~ ( r2 @ A @ C )
| ~ ( good_in_physics @ B @ C )
| ( ( good_in_maths @ B @ ( sk3 @ C @ B @ A ) )
!= ( good_in_maths @ D @ ( sk2 @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[74,71]) ).
thf(462,plain,
! [D: mu,C: $i,B: mu,A: $i] :
( ~ ( r2 @ A @ C )
| ~ ( good_in_physics @ B @ C )
| ( B != D )
| ( ( sk3 @ C @ B @ A )
!= ( sk2 @ D ) ) ),
inference(simp,[status(thm)],[456]) ).
thf(473,plain,
! [C: mu,B: $i,A: $i] :
( ~ ( r2 @ A @ B )
| ~ ( good_in_physics @ C @ B )
| ( ( sk3 @ B @ C @ A )
!= ( sk2 @ C ) ) ),
inference(simp,[status(thm)],[462]) ).
thf(7132,plain,
! [E: mu,D: $i,C: $i,B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ~ ( good_in_physics @ E @ D )
| ( ( sk3 @ D @ E @ C )
!= ( sk2 @ E ) )
| ( ( r2 @ sk1
@ ( sk7
@ ^ [F: $i] :
~ ( r2 @ sk1 @ F )
@ sk1 ) )
!= ( r2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6377,473]) ).
thf(7133,plain,
! [C: mu,B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ~ ( good_in_physics @ C
@ ( sk7
@ ^ [D: $i] :
~ ( r2 @ sk1 @ D )
@ sk1 ) )
| ( ( sk3
@ ( sk7
@ ^ [D: $i] :
~ ( r2 @ sk1 @ D )
@ sk1 )
@ C
@ sk1 )
!= ( sk2 @ C ) ) ),
inference(pattern_uni,[status(thm)],[7132:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( sk7 @ ^ [F: $i] : ~ ( r2 @ sk1 @ F ) @ sk1 )),bind(E,$thf( E ))]]) ).
thf(7285,plain,
! [C: mu,B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ~ ( good_in_physics @ C
@ ( sk7
@ ^ [D: $i] :
~ ( r2 @ sk1 @ D )
@ sk1 ) )
| ( ( sk3
@ ( sk7
@ ^ [D: $i] :
~ ( r2 @ sk1 @ D )
@ sk1 )
@ C
@ sk1 )
!= ( sk2 @ C ) ) ),
inference(simp,[status(thm)],[7133]) ).
thf(7,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r2 @ A ) @ ( mbox @ r2 @ ( mbox @ r2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r2) ).
thf(87,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ! [D: $i] :
( ~ ( r2 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(88,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( r2 @ A @ ( sk8 @ B @ A ) )
| ~ ( r2 @ A @ C )
| ~ ( r2 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[87]) ).
thf(5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r2 @ A ) @ ( mnot @ ( mbox @ r2 @ ( mnot @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r2) ).
thf(79,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) )
| ~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(82,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk5 @ B @ A ) )
| ( r2 @ A @ ( sk6 @ B @ A ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(1897,plain,
! [A: $i] :
( ~ $true
| ( r2 @ A
@ ( sk6
@ ^ [B: $i] : $true
@ A ) ) ),
inference(prim_subst,[status(thm)],[82:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : $true ))]]) ).
thf(1985,plain,
! [A: $i] :
( r2 @ A
@ ( sk6
@ ^ [B: $i] : $true
@ A ) ),
inference(simp,[status(thm)],[1897]) ).
thf(2015,plain,
! [C: $i,B: $i,A: $i] :
( ( mathematician @ tom @ C )
| ( ( r2 @ A
@ ( sk6
@ ^ [D: $i] : $true
@ A ) )
!= ( r2 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1985,138]) ).
thf(2016,plain,
! [A: $i] :
( mathematician @ tom
@ ( sk6
@ ^ [B: $i] : $true
@ A ) ),
inference(pattern_uni,[status(thm)],[2015:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( sk6 @ ^ [E: $i] : $true @ E ))]]) ).
thf(2051,plain,
! [A: $i] :
( mathematician @ tom
@ ( sk6
@ ^ [B: $i] : $true
@ A ) ),
inference(simp,[status(thm)],[2016]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk8 @ B @ A ) )
| ~ ( r2 @ A @ C )
| ~ ( r2 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[87]) ).
thf(5241,plain,
! [E: $i,D: $i,C: $i > $o,B: $i,A: mu] :
( ~ ( C @ ( sk8 @ C @ B ) )
| ~ ( r2 @ D @ E )
| ( C @ E )
| ( ( r2 @ sk1 @ ( sk2 @ A ) )
!= ( r2 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,89]) ).
thf(5242,plain,
! [C: mu,B: $i,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ~ ( r2 @ ( sk2 @ C ) @ B )
| ( A @ B ) ),
inference(pattern_uni,[status(thm)],[5241:[bind(A,$thf( F )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk2 @ F ))]]) ).
thf(5575,plain,
! [C: mu,B: $i,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ~ ( r2 @ ( sk2 @ C ) @ B )
| ( A @ B ) ),
inference(simp,[status(thm)],[5242]) ).
thf(9879,plain,
! [D: mu,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk8 @ B @ sk1 ) )
| ( B @ C )
| ( ( r2 @ A
@ ( sk6
@ ^ [E: $i] : $true
@ A ) )
!= ( r2 @ ( sk2 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1985,5575]) ).
thf(9880,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ( A
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[9879:[bind(A,$thf( sk2 @ H )),bind(B,$thf( B )),bind(C,$thf( sk6 @ ^ [F: $i] : $true @ ( sk2 @ H ) )),bind(D,$thf( H ))]]) ).
thf(10357,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ( A
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ B ) ) ) ),
inference(simp,[status(thm)],[9880]) ).
thf(10687,plain,
! [B: $i > $o,A: mu] :
( ~ ~ ( B
@ ( sk8
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) )
| ~ ( B
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[10357:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(11002,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ A ) ) )
| ( B
@ ( sk8
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) ) ),
inference(cnf,[status(esa)],[10687]) ).
thf(11003,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ A ) ) )
| ( B
@ ( sk8
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) ) ),
inference(simp,[status(thm)],[11002]) ).
thf(13242,plain,
! [C: $i > $o,B: mu,A: $i] :
( ( C
@ ( sk8
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
| ( ( mathematician @ tom
@ ( sk6
@ ^ [D: $i] : $true
@ A ) )
!= ( C
@ ( sk6
@ ^ [D: $i] : $true
@ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2051,11003]) ).
thf(13520,plain,
( mathematician @ tom
@ ( sk8
@ ^ [A: $i] :
~ ( mathematician @ tom @ A )
@ sk1 ) ),
inference(pre_uni,[status(thm)],[13242:[bind(A,$thf( sk2 @ B )),bind(B,$thf( B )),bind(C,$thf( mathematician @ tom ))]]) ).
thf(38,axiom,
mvalid @ ( mbox @ r5 @ ( physics_student @ mike ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a9) ).
thf(184,plain,
! [A: $i,B: $i] :
( ~ ( r5 @ A @ B )
| ( physics_student @ mike @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( r5 @ A @ B )
| ( physics_student @ mike @ B ) ),
inference(cnf,[status(esa)],[184]) ).
thf(31516,plain,
! [B: $i,A: $i] :
( ( physics_student @ mike @ B )
| ( ( r5 @ sk1
@ ( sk15
@ ^ [C: $i] : $false
@ sk1 ) )
!= ( r5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30296,185]) ).
thf(31517,plain,
( physics_student @ mike
@ ( sk15
@ ^ [A: $i] : $false
@ sk1 ) ),
inference(pattern_uni,[status(thm)],[31516:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 @ ^ [C: $i] : $false @ sk1 ))]]) ).
thf(25,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r1 @ A ) @ ( mnot @ ( mbox @ r1 @ ( mnot @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r1) ).
thf(142,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) )
| ~ ! [C: $i] :
( ~ ( r1 @ A @ C )
| ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(81,plain,
! [B: $i > $o,A: $i] :
( ( r2 @ A @ ( sk5 @ B @ A ) )
| ( B @ ( sk6 @ B @ A ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(980,plain,
! [A: $i] :
( ( r2 @ A
@ ( sk5
@ ^ [B: $i] : $false
@ A ) )
| $false ),
inference(prim_subst,[status(thm)],[81:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : $false ))]]) ).
thf(1028,plain,
! [A: $i] :
( r2 @ A
@ ( sk5
@ ^ [B: $i] : $false
@ A ) ),
inference(simp,[status(thm)],[980]) ).
thf(9925,plain,
! [D: mu,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk8 @ B @ sk1 ) )
| ( B @ C )
| ( ( r2 @ A
@ ( sk5
@ ^ [E: $i] : $false
@ A ) )
!= ( r2 @ ( sk2 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1028,5575]) ).
thf(9926,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ( A
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[9925:[bind(A,$thf( sk2 @ H )),bind(B,$thf( B )),bind(C,$thf( sk5 @ ^ [F: $i] : $false @ ( sk2 @ H ) )),bind(D,$thf( H ))]]) ).
thf(10361,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ( A
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) ) ),
inference(simp,[status(thm)],[9926]) ).
thf(11875,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ( ( A
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) )
!= ( ~ ( A @ ( sk8 @ A @ sk1 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10361]) ).
thf(12097,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ( ( A
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) )
!= ( ~ ( A @ ( sk8 @ A @ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[11875]) ).
thf(28,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r3 @ A ) @ ( mbox @ r5 @ ( mbox @ r3 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r5) ).
thf(153,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r5 @ A @ C )
| ! [D: $i] :
( ~ ( r3 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(110,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk15 @ B @ A ) )
| ~ ( r4 @ A @ C )
| ( B @ C ) ),
inference(cnf,[status(esa)],[108]) ).
thf(611,plain,
! [D: mu,C: $i,B: $i,A: mu] :
( ~ ( good_in_physics @ D @ C )
| ( ( sk3 @ C @ D @ B )
!= ( sk2 @ D ) )
| ( ( r2 @ sk1 @ ( sk2 @ A ) )
!= ( r2 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,473]) ).
thf(612,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( ( sk3 @ ( sk2 @ B ) @ A @ sk1 )
!= ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[611:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 @ E ))]]) ).
thf(619,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( ( sk3 @ ( sk2 @ B ) @ A @ sk1 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[612]) ).
thf(21237,plain,
! [D: $i > $o,C: mu,B: $i,A: $i] :
( ~ ( D @ B )
| ( D
@ ( sk7
@ ^ [E: $i] :
~ ( D @ E )
@ sk1 ) )
| ( ( r4 @ A
@ ( sk19
@ ^ [E: $i] : $false
@ A ) )
!= ( r4 @ ( sk2 @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20769,4087]) ).
thf(21238,plain,
! [B: mu,A: $i > $o] :
( ~ ( A
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) )
| ( A
@ ( sk7
@ ^ [C: $i] :
~ ( A @ C )
@ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[21237:[bind(A,$thf( sk2 @ H )),bind(B,$thf( sk19 @ ^ [F: $i] : $false @ ( sk2 @ H ) )),bind(C,$thf( H )),bind(D,$thf( D ))]]) ).
thf(21501,plain,
! [B: mu,A: $i > $o] :
( ~ ( A
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) )
| ( A
@ ( sk7
@ ^ [C: $i] :
~ ( A @ C )
@ sk1 ) ) ),
inference(simp,[status(thm)],[21238]) ).
thf(24429,plain,
! [B: $i > $o,A: mu] :
( ~ ~ ( B
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) )
| ~ ( B
@ ( sk7
@ ^ [C: $i] :
~ ~ ( B @ C )
@ sk1 ) ) ),
inference(prim_subst,[status(thm)],[21501:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(24856,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk7
@ ^ [C: $i] :
~ ~ ( B @ C )
@ sk1 ) )
| ( B
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[24429]) ).
thf(24857,plain,
! [B: $i > $o,A: mu] :
( ~ ( B @ ( sk7 @ B @ sk1 ) )
| ( B
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) ) ),
inference(simp,[status(thm)],[24856]) ).
thf(65,axiom,
mvalid @ ( mbox @ r5 @ ( maths_student @ peter ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a8) ).
thf(265,plain,
! [A: $i,B: $i] :
( ~ ( r5 @ A @ B )
| ( maths_student @ peter @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ~ ( r5 @ A @ B )
| ( maths_student @ peter @ B ) ),
inference(cnf,[status(esa)],[265]) ).
thf(31541,plain,
! [B: $i,A: $i] :
( ( maths_student @ peter @ B )
| ( ( r5 @ sk1
@ ( sk15
@ ^ [C: $i] : $false
@ sk1 ) )
!= ( r5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30296,266]) ).
thf(31542,plain,
( maths_student @ peter
@ ( sk15
@ ^ [A: $i] : $false
@ sk1 ) ),
inference(pattern_uni,[status(thm)],[31541:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 @ ^ [C: $i] : $false @ sk1 ))]]) ).
thf(19,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r2 @ A ) @ ( mbox @ r4 @ ( mbox @ r2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r4) ).
thf(125,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r4 @ A @ C )
| ! [D: $i] :
( ~ ( r2 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(80,plain,
! [B: $i > $o,A: $i] :
( ( r2 @ A @ ( sk5 @ B @ A ) )
| ( r2 @ A @ ( sk6 @ B @ A ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(1481,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( r2 @ A @ ( sk5 @ B @ A ) )
| ( mathematician @ tom @ D )
| ( ( r2 @ A @ ( sk6 @ B @ A ) )
!= ( r2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[80,138]) ).
thf(1482,plain,
! [B: $i,A: $i > $o] :
( ( r2 @ B @ ( sk5 @ A @ B ) )
| ( mathematician @ tom @ ( sk6 @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[1481:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( sk6 @ E @ F ))]]) ).
thf(1514,plain,
! [B: $i,A: $i > $o] :
( ( r2 @ B @ ( sk5 @ A @ B ) )
| ( mathematician @ tom @ ( sk6 @ A @ B ) ) ),
inference(simp,[status(thm)],[1482]) ).
thf(31738,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( r4 @ ( sk2 @ B ) @ A )
| ( ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
!= ( ~ ( C @ A ) ) )
| ( ( physics_student @ mike
@ ( sk15
@ ^ [D: $i] : $false
@ sk1 ) )
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31517,6182]) ).
thf(31843,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( physics_student @ mike
@ ( sk7
@ ^ [B: $i] :
~ ( physics_student @ mike @ B )
@ sk1 ) )
!= ( ~ ( physics_student @ mike
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(pre_uni,[status(thm)],[31738:[bind(A,$thf( sk15 @ ^ [D: $i] : $false @ sk1 )),bind(B,$thf( B )),bind(C,$thf( physics_student @ mike ))]]) ).
thf(31929,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( physics_student @ mike
@ ( sk7
@ ^ [B: $i] :
~ ( physics_student @ mike @ B )
@ sk1 ) )
!= ( ~ ( physics_student @ mike
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[31843]) ).
thf(32590,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( physics_student @ mike
@ ( sk7
@ ^ [B: $i] :
~ ( physics_student @ mike @ B )
@ sk1 ) )
!= ~ $true ) ),
inference(rewrite,[status(thm)],[31929,31517]) ).
thf(32591,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk15
@ ^ [B: $i] : $false
@ sk1 ) )
| ( physics_student @ mike
@ ( sk7
@ ^ [B: $i] :
~ ( physics_student @ mike @ B )
@ sk1 ) ) ),
inference(simp,[status(thm)],[32590]) ).
thf(9,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r1 @ A ) @ ( mbox @ r4 @ ( mbox @ r1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r4) ).
thf(93,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r4 @ A @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r1 @ A ) @ ( mbox @ r3 @ ( mbox @ r1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r3) ).
thf(76,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r3 @ A @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(78,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk4 @ B @ A ) )
| ~ ( r3 @ A @ C )
| ~ ( r1 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[76]) ).
thf(1344,plain,
! [D: mu,C: $i,B: $i,A: $i] :
( ~ ( good_in_physics @ D @ C )
| ( ( sk3 @ C @ D @ B )
!= ( sk2 @ D ) )
| ( ( r2 @ A
@ ( sk5
@ ^ [E: $i] : $false
@ A ) )
!= ( r2 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1028,473]) ).
thf(1345,plain,
! [B: $i,A: mu] :
( ~ ( good_in_physics @ A
@ ( sk5
@ ^ [C: $i] : $false
@ B ) )
| ( ( sk3
@ ( sk5
@ ^ [C: $i] : $false
@ B )
@ A
@ B )
!= ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[1344:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( sk5 @ ^ [F: $i] : $false @ F )),bind(D,$thf( D ))]]) ).
thf(1373,plain,
! [B: $i,A: mu] :
( ~ ( good_in_physics @ A
@ ( sk5
@ ^ [C: $i] : $false
@ B ) )
| ( ( sk3
@ ( sk5
@ ^ [C: $i] : $false
@ B )
@ A
@ B )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[1345]) ).
thf(2549,plain,
! [C: mu,B: $i,A: $i > $o] :
( ( r4 @ sk1 @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( ( A @ B )
!= ( r4 @ sk1 @ ( sk7 @ A @ sk1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2439]) ).
thf(2571,plain,
! [A: mu] :
( ( r4 @ sk1 @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
| ~ ( r4 @ ( sk2 @ A ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[2549:[bind(A,$thf( r4 @ sk1 )),bind(B,$thf( sk7 @ ( r4 @ sk1 ) @ sk1 )),bind(C,$thf( C ))]]) ).
thf(2664,plain,
! [A: mu] :
( ( r4 @ sk1 @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
| ~ ( r4 @ ( sk2 @ A ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[2571]) ).
thf(3240,plain,
! [C: mu,B: $i > $o,A: $i] :
( ( r2 @ A @ ( sk5 @ B @ A ) )
| ( r4 @ sk1 @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( r4 @ ( sk2 @ C ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,2664]) ).
thf(3258,plain,
! [B: $i > mu,A: $i] :
( ( r2 @ A
@ ( sk5
@ ^ [C: $i] : ( r4 @ ( sk2 @ ( B @ C ) ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
@ A ) )
| ( r4 @ sk1 @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[3240:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( r4 @ ( sk2 @ ( H @ E ) ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) ) )),bind(C,$thf( H @ ( sk6 @ ^ [E: $i] : ( r4 @ ( sk2 @ ( H @ E ) ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) ) @ A ) ))]]) ).
thf(3295,plain,
! [B: $i > mu,A: $i] :
( ( r2 @ A
@ ( sk5
@ ^ [C: $i] : ( r4 @ ( sk2 @ ( B @ C ) ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
@ A ) )
| ( r4 @ sk1 @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[3258]) ).
thf(61,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ A ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r3 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r3) ).
thf(253,plain,
! [A: $i,B: $i > $o] :
( ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r3 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r3 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(13,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ A ) @ ( mdia @ r3 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_3) ).
thf(105,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( maths_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r3 @ C @ D )
| ~ ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(106,plain,
! [C: $i,B: mu,A: $i] :
( ~ ( r3 @ A @ C )
| ~ ( maths_student @ B @ C )
| ( good_in_maths @ B @ ( sk14 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ( mathematician @ tom @ C )
| ( ( r2 @ A
@ ( sk5
@ ^ [D: $i] : $false
@ A ) )
!= ( r2 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1028,138]) ).
thf(1338,plain,
! [A: $i] :
( mathematician @ tom
@ ( sk5
@ ^ [B: $i] : $false
@ A ) ),
inference(pattern_uni,[status(thm)],[1337:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( sk5 @ ^ [E: $i] : $false @ E ))]]) ).
thf(1383,plain,
! [A: $i] :
( mathematician @ tom
@ ( sk5
@ ^ [B: $i] : $false
@ A ) ),
inference(simp,[status(thm)],[1338]) ).
thf(26,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r2 @ A ) @ ( mbox @ r1 @ ( mbox @ r2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r1) ).
thf(147,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ! [D: $i] :
( ~ ( r2 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(9630,plain,
! [D: $i,C: $i,B: $i,A: $i > $o] :
( ( mathematician @ tom @ ( sk6 @ A @ B ) )
| ( mathematician @ tom @ D )
| ( ( r2 @ B @ ( sk5 @ A @ B ) )
!= ( r2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1514,138]) ).
thf(9631,plain,
! [B: $i,A: $i > $o] :
( ( mathematician @ tom @ ( sk6 @ A @ B ) )
| ( mathematician @ tom @ ( sk5 @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[9630:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( sk5 @ E @ F ))]]) ).
thf(9796,plain,
! [B: $i,A: $i > $o] :
( ( mathematician @ tom @ ( sk6 @ A @ B ) )
| ( mathematician @ tom @ ( sk5 @ A @ B ) ) ),
inference(simp,[status(thm)],[9631]) ).
thf(50,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r5_r3) ).
thf(221,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(45,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ A ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r1) ).
thf(206,plain,
! [A: $i,B: $i > $o] :
( ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(54,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r5 @ ( mathematician @ A ) ) @ ( mbox @ r5 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_5) ).
thf(233,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r5 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r5 @ C @ D )
| ( mathematician @ B @ D ) )
| ! [D: $i] :
( ~ ( r5 @ C @ D )
| ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(59,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mimplies @ ( maths_teacher @ A ) @ ( mbox @ r4 @ ( good_in_maths @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r1) ).
thf(248,plain,
! [A: $i,B: mu] :
( ~ ( maths_teacher @ B @ A )
| ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( good_in_maths @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(17,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mbox @ r5 @ ( mbox @ r4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r5) ).
thf(117,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r5 @ A @ C )
| ! [D: $i] :
( ~ ( r4 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(67,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r3 @ A ) @ ( mbox @ r1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r3_r1) ).
thf(270,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(12,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ A ) @ ( mdia @ r1 @ ( good_in_physics @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_1) ).
thf(102,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( physics_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ~ ( good_in_physics @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,axiom,
mvalid @ ( maths_teacher @ john ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a6) ).
thf(159,plain,
! [A: $i] : ( maths_teacher @ john @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(160,plain,
! [A: $i] : ( maths_teacher @ john @ A ),
inference(cnf,[status(esa)],[159]) ).
thf(8,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ A ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r2 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r2) ).
thf(90,plain,
! [A: $i,B: $i > $o] :
( ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r2 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C )
| ~ ( r2 @ A @ D )
| ( r2 @ D @ ( sk9 @ D @ B @ A ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(42,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mbox @ r3 @ ( mbox @ r4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r3) ).
thf(197,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r3 @ A @ C )
| ! [D: $i] :
( ~ ( r4 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(10,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mbox @ r1 @ ( mbox @ r4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r1) ).
thf(96,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ! [D: $i] :
( ~ ( r4 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( r4 @ A @ ( sk11 @ B @ A ) )
| ~ ( r1 @ A @ C )
| ~ ( r4 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[96]) ).
thf(51,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r1 @ ( mathematician @ A ) ) @ ( mbox @ r1 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_1) ).
thf(224,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r5 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( mathematician @ B @ D ) )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(29,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r1 @ A ) @ ( mbox @ r1 @ ( mbox @ r1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r1) ).
thf(156,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(33,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r2 @ A ) @ ( mbox @ r1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r2_r1) ).
thf(169,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(77,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( r1 @ A @ ( sk4 @ B @ A ) )
| ~ ( r3 @ A @ C )
| ~ ( r1 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[76]) ).
thf(47,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r3 @ A ) @ ( mbox @ r2 @ ( mbox @ r3 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r2) ).
thf(212,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ! [D: $i] :
( ~ ( r3 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(62,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r2 @ ( mbox @ r5 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r2) ).
thf(256,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ! [D: $i] :
( ~ ( r5 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(22,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r1 @ A ) @ ( mbox @ r5 @ ( mbox @ r1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r5) ).
thf(134,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r5 @ A @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(20,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mbox @ r2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r4_r2) ).
thf(128,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30706,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk15 @ B @ A ) )
| ( B @ C )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [D: $i] : $false
@ sk1 ) )
!= ( r4 @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21225,110]) ).
thf(30707,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk15 @ A @ sk1 ) )
| ( A
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[30706:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk7 @ ^ [D: $i] : $false @ sk1 ))]]) ).
thf(31499,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk15 @ A @ sk1 ) )
| ( A
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ),
inference(simp,[status(thm)],[30707]) ).
thf(33067,plain,
! [B: $i > $o,A: $i > $o] :
( ( A
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
| ( B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
| ( ( r5 @ sk1 @ ( sk15 @ A @ sk1 ) )
!= ( B @ ( sk15 @ B @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29611,31499]) ).
thf(33164,plain,
( ( r5 @ sk1
@ ( sk7
@ ^ [A: $i] : $false
@ sk1 ) )
| ( r5 @ sk1
@ ( sk7
@ ^ [A: $i] : $false
@ sk1 ) ) ),
inference(pre_uni,[status(thm)],[33067:[bind(A,$thf( r5 @ sk1 )),bind(B,$thf( r5 @ sk1 ))]]) ).
thf(33274,plain,
( r5 @ sk1
@ ( sk7
@ ^ [A: $i] : $false
@ sk1 ) ),
inference(simp,[status(thm)],[33164]) ).
thf(32,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r5 @ A ) ) @ ( mbox @ r5 @ ( mnot @ ( mbox @ r5 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r5) ).
thf(166,plain,
! [A: $i,B: $i > $o] :
( ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r5 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r5 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(31,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r3 @ A ) @ ( mnot @ ( mbox @ r3 @ ( mnot @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r3) ).
thf(161,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(40,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r4 @ ( mbox @ r5 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r4) ).
thf(191,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r4 @ A @ C )
| ! [D: $i] :
( ~ ( r5 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(11888,plain,
! [B: $i > $o,A: mu] :
( ~ ~ ( B
@ ( sk8
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) )
| ~ ( B
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[10361:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(12169,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) )
| ( B
@ ( sk8
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) ) ),
inference(cnf,[status(esa)],[11888]) ).
thf(12170,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) )
| ( B
@ ( sk8
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) ) ),
inference(simp,[status(thm)],[12169]) ).
thf(10679,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ( ( A
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ B ) ) )
!= ( ~ ( A @ ( sk8 @ A @ sk1 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10357]) ).
thf(10709,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk8 @ A @ sk1 ) )
| ( ( A
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ B ) ) )
!= ( ~ ( A @ ( sk8 @ A @ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[10679]) ).
thf(21249,plain,
! [D: mu,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk7 @ B @ sk1 ) )
| ( B @ C )
| ( ( r4 @ A
@ ( sk19
@ ^ [E: $i] : $false
@ A ) )
!= ( r4 @ ( sk2 @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20769,3144]) ).
thf(21250,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk7 @ A @ sk1 ) )
| ( A
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[21249:[bind(A,$thf( sk2 @ H )),bind(B,$thf( B )),bind(C,$thf( sk19 @ ^ [F: $i] : $false @ ( sk2 @ H ) )),bind(D,$thf( H ))]]) ).
thf(21425,plain,
! [B: mu,A: $i > $o] :
( ~ ( A @ ( sk7 @ A @ sk1 ) )
| ( A
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ B ) ) ) ),
inference(simp,[status(thm)],[21250]) ).
thf(22852,plain,
! [B: $i > $o,A: mu] :
( ~ ~ ( B
@ ( sk7
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) )
| ~ ( B
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) ) ),
inference(prim_subst,[status(thm)],[21425:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(23244,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) )
| ( B
@ ( sk7
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) ) ),
inference(cnf,[status(esa)],[22852]) ).
thf(23245,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk19
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) )
| ( B
@ ( sk7
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) ) ),
inference(simp,[status(thm)],[23244]) ).
thf(63,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r1 @ A ) @ ( mbox @ r2 @ ( mbox @ r1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r1_r2) ).
thf(259,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(14469,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( r4 @ ( sk2 @ B ) @ A )
| ( ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
!= ( ~ ( C @ A ) ) )
| ( ( mathematician @ tom
@ ( sk8
@ ^ [D: $i] :
~ ( mathematician @ tom @ D )
@ sk1 ) )
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13520,6182]) ).
thf(14499,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk8
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) )
| ( ( mathematician @ tom
@ ( sk7
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) )
!= ( ~ ( mathematician @ tom
@ ( sk8
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) ) ) ) ),
inference(pre_uni,[status(thm)],[14469:[bind(A,$thf( sk8 @ ^ [D: $i] : ~ ( mathematician @ tom @ D ) @ sk1 )),bind(B,$thf( B )),bind(C,$thf( mathematician @ tom ))]]) ).
thf(14502,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk8
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) )
| ( ( mathematician @ tom
@ ( sk7
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) )
!= ( ~ ( mathematician @ tom
@ ( sk8
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[14499]) ).
thf(14507,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk8
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) )
| ( ( mathematician @ tom
@ ( sk7
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) )
!= ~ $true ) ),
inference(rewrite,[status(thm)],[14502,13520]) ).
thf(14508,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk8
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) )
| ( mathematician @ tom
@ ( sk7
@ ^ [B: $i] :
~ ( mathematician @ tom @ B )
@ sk1 ) ) ),
inference(simp,[status(thm)],[14507]) ).
thf(289,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk4 @ B @ A ) )
| ~ ( r3 @ A @ C )
| ~ ( r1 @ C @ D )
| ( ( B @ D )
!= ( ~ ( B @ ( sk4 @ B @ A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[78]) ).
thf(313,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk4 @ B @ A ) )
| ~ ( r3 @ A @ C )
| ~ ( r1 @ C @ D )
| ( ( B @ D )
!= ( ~ ( B @ ( sk4 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[289]) ).
thf(21522,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( C @ A )
| ( ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
!= ( ~ ( C @ A ) ) )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [D: $i] : $false
@ sk1 ) )
!= ( r4 @ ( sk2 @ B ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21225,6182]) ).
thf(21610,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( C @ A )
| ( ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
!= ( ~ ( C @ A ) ) )
| ( ( sk2 @ B )
!= sk1 )
| ( ( sk7
@ ^ [D: $i] : $false
@ sk1 )
!= A ) ),
inference(simp,[status(thm)],[21522]) ).
thf(21725,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
| ( ( B
@ ( sk7
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) )
!= ( ~ ( B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) ) ) )
| ( ( sk2 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[21610]) ).
thf(55,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r3 @ A ) @ ( mbox @ r4 @ ( mbox @ r3 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r4) ).
thf(236,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r4 @ A @ C )
| ! [D: $i] :
( ~ ( r3 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(37,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r45r1) ).
thf(181,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(34,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mbox @ r3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r4_r3) ).
thf(172,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(53,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r3 @ ( mathematician @ A ) ) @ ( mbox @ r3 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_3) ).
thf(230,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r5 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r3 @ C @ D )
| ( mathematician @ B @ D ) )
| ! [D: $i] :
( ~ ( r3 @ C @ D )
| ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(58,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r5_r2) ).
thf(245,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk11 @ B @ A ) )
| ~ ( r1 @ A @ C )
| ~ ( r4 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[96]) ).
thf(103,plain,
! [C: $i,B: mu,A: $i] :
( ~ ( r3 @ A @ C )
| ~ ( physics_student @ B @ C )
| ( good_in_physics @ B @ ( sk13 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[102]) ).
thf(91,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C )
| ~ ( r2 @ A @ D )
| ~ ( B @ ( sk9 @ D @ B @ A ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(2550,plain,
! [C: mu,B: $i,A: $i > $o] :
( ( r4 @ sk1 @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( ( A @ B )
!= ( ~ ( r4 @ ( sk2 @ C ) @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2439]) ).
thf(2628,plain,
! [A: mu] :
( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B @ B )
@ sk1 ) )
| ~ ( r4 @ ( sk2 @ A ) @ ( sk2 @ A ) ) ),
inference(pre_uni,[status(thm)],[2550:[bind(A,$thf( ^ [D: $i] : ~ ( r4 @ D @ D ) )),bind(B,$thf( sk2 @ C )),bind(C,$thf( C ))]]) ).
thf(2710,plain,
! [A: mu] :
( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B @ B )
@ sk1 ) )
| ~ ( r4 @ ( sk2 @ A ) @ ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[2628]) ).
thf(6012,plain,
! [D: $i > $o,C: mu,B: $i,A: $i] :
( ~ ( r4 @ ( sk2 @ C ) @ B )
| ( D
@ ( sk7
@ ^ [E: $i] :
~ ( D @ E )
@ sk1 ) )
| ( ( mathematician @ tom
@ ( sk5
@ ^ [E: $i] : $false
@ A ) )
!= ( D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1383,4087]) ).
thf(6295,plain,
! [B: mu,A: $i] :
( ~ ( r4 @ ( sk2 @ B )
@ ( sk5
@ ^ [C: $i] : $false
@ A ) )
| ( mathematician @ tom
@ ( sk7
@ ^ [C: $i] :
~ ( mathematician @ tom @ C )
@ sk1 ) ) ),
inference(pre_uni,[status(thm)],[6012:[bind(A,$thf( A )),bind(B,$thf( sk5 @ ^ [E: $i] : $false @ A )),bind(C,$thf( C )),bind(D,$thf( mathematician @ tom ))]]) ).
thf(6449,plain,
! [B: mu,A: $i] :
( ~ ( r4 @ ( sk2 @ B )
@ ( sk5
@ ^ [C: $i] : $false
@ A ) )
| ( mathematician @ tom
@ ( sk7
@ ^ [C: $i] :
~ ( mathematician @ tom @ C )
@ sk1 ) ) ),
inference(simp,[status(thm)],[6295]) ).
thf(276,plain,
! [C: $i,B: $i,A: mu] :
( ( mathematician @ tom @ C )
| ( ( r2 @ sk1 @ ( sk2 @ A ) )
!= ( r2 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,138]) ).
thf(277,plain,
! [A: mu] : ( mathematician @ tom @ ( sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( D )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 @ D ))]]) ).
thf(278,plain,
! [A: mu] : ( mathematician @ tom @ ( sk2 @ A ) ),
inference(simp,[status(thm)],[277]) ).
thf(2009,plain,
! [D: mu,C: $i,B: $i,A: $i] :
( ~ ( good_in_physics @ D @ C )
| ( ( sk3 @ C @ D @ B )
!= ( sk2 @ D ) )
| ( ( r2 @ A
@ ( sk6
@ ^ [E: $i] : $true
@ A ) )
!= ( r2 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1985,473]) ).
thf(2010,plain,
! [B: $i,A: mu] :
( ~ ( good_in_physics @ A
@ ( sk6
@ ^ [C: $i] : $true
@ B ) )
| ( ( sk3
@ ( sk6
@ ^ [C: $i] : $true
@ B )
@ A
@ B )
!= ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[2009:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( sk6 @ ^ [F: $i] : $true @ F )),bind(D,$thf( D ))]]) ).
thf(2064,plain,
! [B: $i,A: mu] :
( ~ ( good_in_physics @ A
@ ( sk6
@ ^ [C: $i] : $true
@ B ) )
| ( ( sk3
@ ( sk6
@ ^ [C: $i] : $true
@ B )
@ A
@ B )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[2010]) ).
thf(66,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ A ) @ ( mdia @ r4 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_4) ).
thf(267,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( maths_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r4 @ C @ D )
| ~ ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(454,plain,
! [D: $i,C: mu,B: $i,A: mu] :
( ~ ( good_in_physics @ C @ D )
| ( good_in_maths @ C @ ( sk3 @ D @ C @ B ) )
| ( ( r2 @ sk1 @ ( sk2 @ A ) )
!= ( r2 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,74]) ).
thf(455,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( good_in_maths @ A @ ( sk3 @ ( sk2 @ B ) @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[454:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk2 @ E ))]]) ).
thf(470,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( good_in_maths @ A @ ( sk3 @ ( sk2 @ B ) @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[455]) ).
thf(638,plain,
! [C: mu,B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( ( good_in_maths @ A @ ( sk3 @ ( sk2 @ B ) @ A @ sk1 ) )
!= ( good_in_maths @ C @ ( sk2 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[470,71]) ).
thf(642,plain,
! [C: mu,B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( A != C )
| ( ( sk3 @ ( sk2 @ B ) @ A @ sk1 )
!= ( sk2 @ C ) ) ),
inference(simp,[status(thm)],[638]) ).
thf(653,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ B @ ( sk2 @ A ) )
| ( ( sk3 @ ( sk2 @ A ) @ B @ sk1 )
!= ( sk2 @ B ) ) ),
inference(simp,[status(thm)],[642]) ).
thf(46,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mbox @ r1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r4_r1) ).
thf(209,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(15,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r3 @ A ) @ ( mbox @ r3 @ ( mbox @ r3 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r3) ).
thf(111,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r3 @ A @ C )
| ! [D: $i] :
( ~ ( r3 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( r3 @ A @ ( sk16 @ B @ A ) )
| ~ ( r3 @ A @ C )
| ~ ( r3 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[111]) ).
thf(7136,plain,
! [D: $i,C: $i,B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ( mathematician @ tom @ D )
| ( ( r2 @ sk1
@ ( sk7
@ ^ [E: $i] :
~ ( r2 @ sk1 @ E )
@ sk1 ) )
!= ( r2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6377,138]) ).
thf(7137,plain,
! [B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ( mathematician @ tom
@ ( sk7
@ ^ [C: $i] :
~ ( r2 @ sk1 @ C )
@ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7136:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( sk7 @ ^ [E: $i] : ~ ( r2 @ sk1 @ E ) @ sk1 ))]]) ).
thf(41,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ A ) @ ( mdia @ r5 @ ( good_in_physics @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_5) ).
thf(194,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( physics_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r5 @ C @ D )
| ~ ( good_in_physics @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r2 @ A ) @ ( mbox @ r3 @ ( mbox @ r2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r3) ).
thf(150,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r3 @ A @ C )
| ! [D: $i] :
( ~ ( r2 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( B @ ( sk10 @ B @ A ) )
| ~ ( r4 @ A @ C )
| ~ ( r1 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[93]) ).
thf(21521,plain,
! [C: $i > $o,B: mu,A: $i] :
( ~ ( r4 @ ( sk2 @ B ) @ A )
| ( ( C
@ ( sk7
@ ^ [D: $i] :
~ ( C @ D )
@ sk1 ) )
!= ( ~ ( C @ A ) ) )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [D: $i] : $false
@ sk1 ) )
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21225,6182]) ).
thf(21621,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ sk1 )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1
@ ( sk7
@ ^ [C: $i] : $false
@ B ) )
@ sk1 ) ) )
!= ( ~ ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(pre_uni,[status(thm)],[21521:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( ^ [D: $i] : ( r4 @ sk1 @ ( sk7 @ ^ [E: $i] : $false @ D ) ) ))]]) ).
thf(21733,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ sk1 )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1
@ ( sk7
@ ^ [C: $i] : $false
@ B ) )
@ sk1 ) ) )
!= ( ~ ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[21621]) ).
thf(22141,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ sk1 )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1
@ ( sk7
@ ^ [C: $i] : $false
@ B ) )
@ sk1 ) ) )
!= ~ $true ) ),
inference(rewrite,[status(thm)],[21733,21225]) ).
thf(22142,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ sk1 )
| ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1
@ ( sk7
@ ^ [C: $i] : $false
@ B ) )
@ sk1 ) ) ) ),
inference(simp,[status(thm)],[22141]) ).
thf(6055,plain,
! [D: $i > $o,C: mu,B: $i,A: $i] :
( ~ ( r4 @ ( sk2 @ C ) @ B )
| ( D
@ ( sk7
@ ^ [E: $i] :
~ ( D @ E )
@ sk1 ) )
| ( ( mathematician @ tom
@ ( sk6
@ ^ [E: $i] : $true
@ A ) )
!= ( D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2051,4087]) ).
thf(6331,plain,
! [B: mu,A: $i] :
( ~ ( r4 @ ( sk2 @ B )
@ ( sk6
@ ^ [C: $i] : $true
@ A ) )
| ( mathematician @ tom
@ ( sk7
@ ^ [C: $i] :
~ ( mathematician @ tom @ C )
@ sk1 ) ) ),
inference(pre_uni,[status(thm)],[6055:[bind(A,$thf( A )),bind(B,$thf( sk6 @ ^ [E: $i] : $true @ A )),bind(C,$thf( C )),bind(D,$thf( mathematician @ tom ))]]) ).
thf(6472,plain,
! [B: mu,A: $i] :
( ~ ( r4 @ ( sk2 @ B )
@ ( sk6
@ ^ [C: $i] : $true
@ A ) )
| ( mathematician @ tom
@ ( sk7
@ ^ [C: $i] :
~ ( mathematician @ tom @ C )
@ sk1 ) ) ),
inference(simp,[status(thm)],[6331]) ).
thf(75,plain,
! [C: $i,B: mu,A: $i] :
( ~ ( r2 @ A @ C )
| ~ ( good_in_physics @ B @ C )
| ( r2 @ C @ ( sk3 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(670,plain,
! [D: $i,C: mu,B: $i,A: mu] :
( ~ ( good_in_physics @ C @ D )
| ( r2 @ D @ ( sk3 @ D @ C @ B ) )
| ( ( r2 @ sk1 @ ( sk2 @ A ) )
!= ( r2 @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,75]) ).
thf(671,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( r2 @ ( sk2 @ B ) @ ( sk3 @ ( sk2 @ B ) @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[670:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk2 @ E ))]]) ).
thf(703,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( r2 @ ( sk2 @ B ) @ ( sk3 @ ( sk2 @ B ) @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[671]) ).
thf(35,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ A ) @ ( mdia @ r1 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_1) ).
thf(175,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( maths_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ~ ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(60,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r3 @ A ) @ ( mbox @ r2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_r3_r2) ).
thf(250,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(44,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r2 @ A ) @ ( mbox @ r5 @ ( mbox @ r2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r2_r5) ).
thf(203,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r2 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r5 @ A @ C )
| ! [D: $i] :
( ~ ( r2 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(5844,plain,
! [D: $i,C: $i,B: $i > mu,A: $i] :
( ( r4 @ sk1 @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
| ( mathematician @ tom @ D )
| ( ( r2 @ A
@ ( sk5
@ ^ [E: $i] : ( r4 @ ( sk2 @ ( B @ E ) ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
@ A ) )
!= ( r2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[3295,138]) ).
thf(5845,plain,
! [B: $i > mu,A: $i] :
( ( r4 @ sk1 @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
| ( mathematician @ tom
@ ( sk5
@ ^ [C: $i] : ( r4 @ ( sk2 @ ( B @ C ) ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
@ A ) ) ),
inference(pattern_uni,[status(thm)],[5844:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( F )),bind(D,$thf( sk5 @ ^ [G: $i] : ( r4 @ ( sk2 @ ( I @ G ) ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) ) @ F ))]]) ).
thf(5934,plain,
! [B: $i > mu,A: $i] :
( ( r4 @ sk1 @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
| ( mathematician @ tom
@ ( sk5
@ ^ [C: $i] : ( r4 @ ( sk2 @ ( B @ C ) ) @ ( sk7 @ ( r4 @ sk1 ) @ sk1 ) )
@ A ) ) ),
inference(simp,[status(thm)],[5845]) ).
thf(49,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ A ) @ ( mdia @ r4 @ ( good_in_physics @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_4) ).
thf(218,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( physics_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r4 @ C @ D )
| ~ ( good_in_physics @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(104,plain,
! [C: $i,B: mu,A: $i] :
( ~ ( r3 @ A @ C )
| ~ ( physics_student @ B @ C )
| ( r1 @ C @ ( sk13 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[102]) ).
thf(6056,plain,
! [D: $i > $o,C: mu,B: $i,A: mu] :
( ~ ( r4 @ ( sk2 @ C ) @ B )
| ( D
@ ( sk7
@ ^ [E: $i] :
~ ( D @ E )
@ sk1 ) )
| ( ( mathematician @ tom @ ( sk2 @ A ) )
!= ( D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[278,4087]) ).
thf(6288,plain,
! [B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ( mathematician @ tom
@ ( sk7
@ ^ [C: $i] :
~ ( mathematician @ tom @ C )
@ sk1 ) ) ),
inference(pre_uni,[status(thm)],[6056:[bind(A,$thf( A )),bind(B,$thf( sk2 @ A )),bind(C,$thf( C )),bind(D,$thf( mathematician @ tom ))]]) ).
thf(6447,plain,
! [B: mu,A: mu] :
( ~ ( r4 @ ( sk2 @ B ) @ ( sk2 @ A ) )
| ( mathematician @ tom
@ ( sk7
@ ^ [C: $i] :
~ ( mathematician @ tom @ C )
@ sk1 ) ) ),
inference(simp,[status(thm)],[6288]) ).
thf(21622,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ sk1 )
| ( ( r4
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
@ sk1 )
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) )
!= ( ~ ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(pre_uni,[status(thm)],[21521:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( ^ [D: $i] : ( r4 @ D @ ( sk7 @ ^ [E: $i] : $false @ sk1 ) ) ))]]) ).
thf(21734,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ sk1 )
| ( ( r4
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
@ sk1 )
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) )
!= ( ~ ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[21622]) ).
thf(23700,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ sk1 )
| ( ( r4
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
@ sk1 )
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) )
!= ~ $true ) ),
inference(rewrite,[status(thm)],[21734,21225]) ).
thf(23701,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ sk1 )
| ( r4
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
@ sk1 )
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ),
inference(simp,[status(thm)],[23700]) ).
thf(39,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mnot @ ( mbox @ r5 @ ( mnot @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_r5) ).
thf(186,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(16,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r3 @ A ) @ ( mbox @ r1 @ ( mbox @ r3 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r3_r1) ).
thf(114,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r3 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ! [D: $i] :
( ~ ( r3 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r4 @ A ) @ ( mbox @ r4 @ ( mbox @ r4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r4_r4) ).
thf(139,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r4 @ A @ C )
| ! [D: $i] :
( ~ ( r4 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3805,plain,
! [C: mu,B: $i,A: $i > $o] :
( ~ ( A @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( ( A @ B )
!= ( ~ ( r4 @ ( sk2 @ C ) @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3144]) ).
thf(3974,plain,
! [A: mu] :
( ~ ~ ( r4
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B @ B )
@ sk1 )
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B @ B )
@ sk1 ) )
| ~ ( r4 @ ( sk2 @ A ) @ ( sk2 @ A ) ) ),
inference(pre_uni,[status(thm)],[3805:[bind(A,$thf( ^ [D: $i] : ~ ( r4 @ D @ D ) )),bind(B,$thf( sk2 @ C )),bind(C,$thf( C ))]]) ).
thf(4073,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ ( sk2 @ A ) )
| ( r4
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B @ B )
@ sk1 )
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B @ B )
@ sk1 ) ) ),
inference(cnf,[status(esa)],[3974]) ).
thf(4074,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A ) @ ( sk2 @ A ) )
| ( r4
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B @ B )
@ sk1 )
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ B @ B )
@ sk1 ) ) ),
inference(simp,[status(thm)],[4073]) ).
thf(83,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk5 @ B @ A ) )
| ( B @ ( sk6 @ B @ A ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(525,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk5 @ B @ A ) )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( B @ ( sk5 @ B @ A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[83]) ).
thf(549,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk5 @ B @ A ) )
| ( ( B @ ( sk6 @ B @ A ) )
!= ( ~ ( B @ ( sk5 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[525]) ).
thf(64,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ A ) @ ( mdia @ r3 @ ( good_in_physics @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_3) ).
thf(262,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( physics_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r3 @ C @ D )
| ~ ( good_in_physics @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(146,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk26 @ B @ A ) )
| ( B @ ( sk27 @ B @ A ) ) ),
inference(cnf,[status(esa)],[142]) ).
thf(68,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r4 @ ( mathematician @ A ) ) @ ( mbox @ r4 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_4) ).
thf(273,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r5 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r4 @ C @ D )
| ( mathematician @ B @ D ) )
| ! [D: $i] :
( ~ ( r4 @ C @ D )
| ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(13307,plain,
! [B: $i > $o,A: mu] :
( ~ ~ ( B
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ A ) ) )
| ~ ( B
@ ( sk8
@ ^ [C: $i] :
~ ~ ( B @ C )
@ sk1 ) ) ),
inference(prim_subst,[status(thm)],[11003:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(13700,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk8
@ ^ [C: $i] :
~ ~ ( B @ C )
@ sk1 ) )
| ( B
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[13307]) ).
thf(13701,plain,
! [B: $i > $o,A: mu] :
( ~ ( B @ ( sk8 @ B @ sk1 ) )
| ( B
@ ( sk6
@ ^ [C: $i] : $true
@ ( sk2 @ A ) ) ) ),
inference(simp,[status(thm)],[13700]) ).
thf(107,plain,
! [C: $i,B: mu,A: $i] :
( ~ ( r3 @ A @ C )
| ~ ( maths_student @ B @ C )
| ( r3 @ C @ ( sk14 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( r1 @ A @ ( sk10 @ B @ A ) )
| ~ ( r4 @ A @ C )
| ~ ( r1 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[93]) ).
thf(57,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r1 @ ( mbox @ r5 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r1) ).
thf(242,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r1 @ A @ C )
| ! [D: $i] :
( ~ ( r5 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(56,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r4 @ A ) ) @ ( mbox @ r4 @ ( mnot @ ( mbox @ r4 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_r4) ).
thf(239,plain,
! [A: $i,B: $i > $o] :
( ! [C: $i] :
( ~ ( r4 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r4 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r4 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1047,plain,
! [D: $i,C: $i,B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( mathematician @ tom @ D )
| ( ( r2 @ ( sk2 @ B ) @ ( sk3 @ ( sk2 @ B ) @ A @ sk1 ) )
!= ( r2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[703,138]) ).
thf(1048,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( mathematician @ tom @ ( sk3 @ ( sk2 @ B ) @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1047:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( sk2 @ I )),bind(D,$thf( sk3 @ ( sk2 @ I ) @ G @ sk1 ))]]) ).
thf(1093,plain,
! [B: mu,A: mu] :
( ~ ( good_in_physics @ A @ ( sk2 @ B ) )
| ( mathematician @ tom @ ( sk3 @ ( sk2 @ B ) @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[1048]) ).
thf(3804,plain,
! [C: mu,B: $i,A: $i > $o] :
( ~ ( A @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( ( A @ B )
!= ( ~ ( A @ ( sk7 @ A @ sk1 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3144]) ).
thf(3965,plain,
! [C: mu,B: $i,A: $i > $o] :
( ~ ( A @ ( sk7 @ A @ sk1 ) )
| ~ ( r4 @ ( sk2 @ C ) @ B )
| ( ( A @ B )
!= ( ~ ( A @ ( sk7 @ A @ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[3804]) ).
thf(21,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r5 @ ( mimplies @ ( mbox @ r2 @ ( mathematician @ A ) ) @ ( mbox @ r2 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r2_2) ).
thf(131,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r5 @ A @ C )
| ~ ! [D: $i] :
( ~ ( r2 @ C @ D )
| ( mathematician @ B @ D ) )
| ! [D: $i] :
( ~ ( r2 @ C @ D )
| ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15436,plain,
! [B: $i > $o,A: mu] :
( ~ ~ ( B
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) )
| ~ ( B
@ ( sk8
@ ^ [C: $i] :
~ ~ ( B @ C )
@ sk1 ) ) ),
inference(prim_subst,[status(thm)],[12170:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(15708,plain,
! [B: $i > $o,A: mu] :
( ~ ( B
@ ( sk8
@ ^ [C: $i] :
~ ~ ( B @ C )
@ sk1 ) )
| ( B
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[15436]) ).
thf(15709,plain,
! [B: $i > $o,A: mu] :
( ~ ( B @ ( sk8 @ B @ sk1 ) )
| ( B
@ ( sk5
@ ^ [C: $i] : $false
@ ( sk2 @ A ) ) ) ),
inference(simp,[status(thm)],[15708]) ).
thf(43,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( physics_student @ A ) @ ( mdia @ r2 @ ( good_in_physics @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r4_2) ).
thf(200,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( physics_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r2 @ C @ D )
| ~ ( good_in_physics @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ r5 @ A ) @ ( mbox @ r5 @ ( mbox @ r5 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_r5_r5) ).
thf(178,plain,
! [A: $i,B: $i > $o] :
( ~ ! [C: $i] :
( ~ ( r5 @ A @ C )
| ( B @ C ) )
| ! [C: $i] :
( ~ ( r5 @ A @ C )
| ! [D: $i] :
( ~ ( r5 @ C @ D )
| ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1580,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk26 @ B @ A ) )
| ( ( B @ ( sk27 @ B @ A ) )
!= ( ~ ( B @ ( sk26 @ B @ A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[146]) ).
thf(1621,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( sk26 @ B @ A ) )
| ( ( B @ ( sk27 @ B @ A ) )
!= ( ~ ( B @ ( sk26 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[1580]) ).
thf(52,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ A ) @ ( mdia @ r2 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_2) ).
thf(227,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( maths_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r2 @ C @ D )
| ~ ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(48,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mbox @ r3 @ ( mimplies @ ( maths_student @ A ) @ ( mdia @ r5 @ ( good_in_maths @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_r3_5) ).
thf(215,plain,
! [A: $i,B: mu,C: $i] :
( ~ ( r3 @ A @ C )
| ~ ( maths_student @ B @ C )
| ~ ! [D: $i] :
( ~ ( r5 @ C @ D )
| ~ ( good_in_maths @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(21619,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1 @ B )
@ sk1 ) )
!= ( ~ ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(pre_uni,[status(thm)],[21521:[bind(A,$thf( sk7 @ ^ [D: $i] : $false @ sk1 )),bind(B,$thf( B )),bind(C,$thf( r4 @ sk1 ))]]) ).
thf(21732,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1 @ B )
@ sk1 ) )
!= ( ~ ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[21619]) ).
thf(21743,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1 @ B )
@ sk1 ) )
!= ~ $true ) ),
inference(rewrite,[status(thm)],[21732,21225]) ).
thf(21744,plain,
! [A: mu] :
( ~ ( r4 @ ( sk2 @ A )
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) )
| ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1 @ B )
@ sk1 ) ) ),
inference(simp,[status(thm)],[21743]) ).
thf(25430,plain,
! [B: $i > $o,A: mu] :
( ( ( B
@ ( sk7
@ ^ [C: $i] :
~ ( B @ C )
@ sk1 ) )
!= ( ~ ( B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) ) ) )
| ( ( sk2 @ A )
!= sk1 )
| ( ( r4 @ sk1
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) )
!= ( B
@ ( sk7
@ ^ [C: $i] : $false
@ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21225,21725]) ).
thf(25669,plain,
! [A: mu] :
( ( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1 @ B )
@ sk1 ) )
!= ( ~ ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] : $false
@ sk1 ) ) ) )
| ( ( sk2 @ A )
!= sk1 ) ),
inference(pre_uni,[status(thm)],[25430:[bind(A,$thf( A )),bind(B,$thf( r4 @ sk1 ))]]) ).
thf(27823,plain,
! [A: mu] :
( ( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1 @ B )
@ sk1 ) )
!= ~ $true )
| ( ( sk2 @ A )
!= sk1 ) ),
inference(rewrite,[status(thm)],[25669,21225]) ).
thf(27824,plain,
! [A: mu] :
( ( r4 @ sk1
@ ( sk7
@ ^ [B: $i] :
~ ( r4 @ sk1 @ B )
@ sk1 ) )
| ( ( sk2 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[27823]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ( r5 @ A @ ( sk12 @ B @ A ) )
| ~ ( r3 @ A @ C )
| ~ ( r5 @ C @ D )
| ( B @ D ) ),
inference(cnf,[status(esa)],[99]) ).
thf(50178,plain,
$false,
inference(e,[status(thm)],[32158,69,138,101,21450,777,7285,88,13520,31517,120,142,12097,153,185,6182,1985,184,110,619,24857,31542,125,1514,32591,93,78,1373,3295,253,106,1383,84,147,9796,221,4087,89,265,74,206,233,248,117,270,85,102,160,11003,137,92,197,97,3144,224,156,169,1028,124,77,212,96,109,256,134,73,128,105,266,33274,30296,166,161,191,12170,10709,23245,259,71,14508,29611,313,21725,236,181,10361,86,159,172,81,230,76,245,98,103,91,2664,108,2710,2439,6377,6449,2051,278,2064,5575,267,80,653,473,21425,209,112,7137,194,150,95,21501,22142,6472,21225,470,703,72,175,250,87,203,5934,218,104,31499,6447,99,23701,186,114,139,75,4074,549,10357,82,262,146,273,13701,107,79,94,242,20769,239,1093,3965,131,15709,200,178,1621,227,122,83,215,21744,27824,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : AGT029^1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 04:13:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.05 % [INFO] Parsing done (186ms).
% 1.47/1.06 % [INFO] Running in sequential loop mode.
% 2.00/1.26 % [INFO] eprover registered as external prover.
% 2.00/1.26 % [INFO] Scanning for conjecture ...
% 2.31/1.39 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.48/1.44 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.79/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 2.79/1.49 % [INFO] Type checking passed.
% 2.79/1.49 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 84.97/20.40 % External prover 'e' found a proof!
% 84.97/20.40 % [INFO] Killing All external provers ...
% 84.97/20.40 % Time passed: 19874ms (effective reasoning time: 19339ms)
% 84.97/20.40 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 84.97/20.40 % Axioms used in derivation (66): axiom_I_for_r4_r1, axiom_4s_for_r1_r1, axiom_4s_for_r5_r1, axiom_r4_4, axiom_4s_for_r3_r1, axiom_4s_for_r5_r2, axiom_4s_for_r3_r2, axiom_4s_for_r3_r4, axiom_5_for_r5, axiom_r2_3, axiom_I_for_r45r1, axiom_D_for_r5, axiom_I_for_r5_r3, axiom_4s_for_r4_r3, axiom_4s_for_r5_r5, axiom_r3_1, axiom_D_for_r2, axiom_r4_2, axiom_4s_for_r5_r4, axiom_4s_for_r4_r2, axiom_4s_for_r1_r4, axiom_4s_for_r2_r1, axiom_4s_for_r3_r3, axiom_4s_for_r4_r4, axiom_4s_for_r2_r5, axiom_r3_5, axiom_I_for_r4_r2, axiom_D_for_r4, axiom_I_for_r2_r1, axiom_4s_for_r2_r2, axiom_r1, axiom_a6, axiom_I_for_r3_r1, axiom_r2_2, axiom_I_for_r5_r4, axiom_r4_1, axiom_4s_for_r5_r3, axiom_r2_5, axiom_r3_4, axiom_5_for_r3, axiom_5_for_r2, axiom_I_for_r4_r3, axiom_r5, axiom_4s_for_r1_r5, axiom_D_for_r3, axiom_a7, axiom_a8, axiom_4s_for_r1_r2, axiom_r4_5, axiom_I_for_r3_r2, axiom_4s_for_r2_r4, axiom_4s_for_r3_r5, axiom_r2_1, axiom_5_for_r4, axiom_r3_2, axiom_r2_4, axiom_5_for_r1, axiom_4s_for_r2_r3, axiom_I_for_r5_r2, axiom_r4_3, axiom_4s_for_r4_r5, axiom_4s_for_r1_r3, axiom_r3_3, axiom_4s_for_r4_r1, axiom_D_for_r1, axiom_a9
% 84.97/20.40 % No. of inferences in proof: 368
% 84.97/20.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19874 ms resp. 19339 ms w/o parsing
% 85.51/20.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 85.51/20.54 % [INFO] Killing All external provers ...
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