%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP010+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:11:20 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 7 ( 18 avg)
% Number of connectives : 153 ( 45 ~; 0 |; 0 &)
% ( 48 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 46 ( 46 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 56 ( 52 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: $i > $o ).
tff(ap_type,type,
ap: ( $i * $i ) > $i ).
tff(c_2Ecardinal_2Ecardleq_type,type,
c_2Ecardinal_2Ecardleq: ( $i * $i ) > $i ).
tff(mem_type,type,
mem: ( $i * $i ) > $o ).
tff(arr_type,type,
arr: ( $i * $i ) > $i ).
tff(bool_type,type,
bool: $i ).
tff(ne_type,type,
ne: $i > $o ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ! [A_27a: $i] : $true
<=> $true ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(3,plain,
^ [A_27a: $i] :
trans(monotonicity(trans(quant_intro(proof_bind(^ [A_27b: $i] :
trans(monotonicity(trans(quant_intro(proof_bind(^ [V0s: $i] :
trans(monotonicity(trans(quant_intro(proof_bind(^ [V1t: $i] :
trans(monotonicity(rewrite(( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
<=> $true )),
( ( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) )
<=> ( mem(V1t,arr(A_27b,bool))
=> $true ) )),
rewrite(( ( mem(V1t,arr(A_27b,bool))
=> $true )
<=> $true )),
( ( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) )
<=> $true ))),
( ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) )
<=> ! [V1t: $i] : $true )),
elim_unused(( ! [V1t: $i] : $true
<=> $true )),
( ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) )
<=> $true )),
( ( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) )
<=> ( mem(V0s,arr(A_27a,bool))
=> $true ) )),
rewrite(( ( mem(V0s,arr(A_27a,bool))
=> $true )
<=> $true )),
( ( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) )
<=> $true ))),
( ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) )
<=> ! [V0s: $i] : $true )),
elim_unused(( ! [V0s: $i] : $true
<=> $true )),
( ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) )
<=> $true )),
( ( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) )
<=> ( ne(A_27b)
=> $true ) )),
rewrite(( ( ne(A_27b)
=> $true )
<=> $true )),
( ( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) )
<=> $true ))),
( ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) )
<=> ! [A_27b: $i] : $true )),
elim_unused(( ! [A_27b: $i] : $true
<=> $true )),
( ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) )
<=> $true )),
( ( ne(A_27a)
=> ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) )
<=> ( ne(A_27a)
=> $true ) )),
rewrite(( ( ne(A_27a)
=> $true )
<=> $true )),
( ( ne(A_27a)
=> ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) )
<=> $true )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [A_27a: $i] :
( ne(A_27a)
=> ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) )
<=> ! [A_27a: $i] : $true ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [A_27a: $i] :
( ne(A_27a)
=> ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
( ~ ! [A_27a: $i] :
( ne(A_27a)
=> ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ~ ! [A_27a: $i] :
( ne(A_27a)
=> ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[6,1]) ).
tff(8,axiom,
~ ! [A_27a: $i] :
( ne(A_27a)
=> ! [A_27b: $i] :
( ne(A_27b)
=> ! [V0s: $i] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t: $i] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
tff(9,plain,
$false,
inference(modus_ponens,[status(thm)],[8,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP010+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 18:09:26 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------