%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG361-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 04:58:59 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.51s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 164 ( 78 ~; 74 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-5 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(c_SEQ_Osubseq_type,type,
c_SEQ_Osubseq: $i > $o ).
tff(v_sko__CHAINED__1_type,type,
v_sko__CHAINED__1: $i > $i ).
tff(v_s_type,type,
v_s: $i ).
tff(c_SEQ_Omonoseq_type,type,
c_SEQ_Omonoseq: $i > $o ).
tff(c_COMBB_type,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Complex_ORe_type,type,
c_Complex_ORe: $i ).
tff(1,plain,
( ~ v_thesis____
<=> ~ v_thesis____ ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ v_thesis____,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
<=> c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(6,plain,
c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
<=> c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
tff(9,plain,
c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_f: $i] :
refl(( ( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
<=> ( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
<=> ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
<=> ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V_f: $i] :
rewrite(( ( v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Osubseq(V_f) )
<=> ( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_f: $i] :
( v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Osubseq(V_f) )
<=> ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_f: $i] :
( v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Osubseq(V_f) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
tff(16,plain,
! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
| v_thesis____
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
<=> ( ~ ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
| v_thesis____
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
<=> ( v_thesis____
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
<=> ( ~ ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
| v_thesis____
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
<=> ( ~ ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
| v_thesis____
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_f: $i] :
( ~ c_SEQ_Osubseq(V_f)
| v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) )
| v_thesis____
| ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG361-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 11:09:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.51 % SZS status Unsatisfiable
% 0.18/0.51 % SZS output start Proof
% See solution above
% 0.18/0.54 % E exiting
%------------------------------------------------------------------------------