%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ038-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:23:15 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.39s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 35 ~; 23 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 12 avg)
% Maximal term depth : 6 ( 2 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 : 3 ( 2 usr; 1 prp; 0-12 aty)
% Number of functors : 14 ( 14 usr; 1 con; 0-2 aty)
% Number of variables : 266 ( 243 !; 0 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
tff(state_type,type,
state: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(e2_type,type,
e2: ( $i * $i ) > $i ).
tff(s_type,type,
s: $i > $i ).
tff(o_type,type,
o: $i ).
tff(e1_type,type,
e1: ( $i * $i ) > $i ).
tff(s4_type,type,
s4: ( $i * $i ) > $i ).
tff(s3_type,type,
s3: ( $i * $i ) > $i ).
tff(s2_type,type,
s2: ( $i * $i ) > $i ).
tff(s1_type,type,
s1: ( $i * $i ) > $i ).
tff(h_type,type,
h: ( $i * $i ) > $i ).
tff(v4_type,type,
v4: ( $i * $i ) > $i ).
tff(v3_type,type,
v3: ( $i * $i ) > $i ).
tff(v2_type,type,
v2: ( $i * $i ) > $i ).
tff(v1_type,type,
v1: ( $i * $i ) > $i ).
tff(bb_type,type,
bb: ( $i * $i ) > $i ).
tff(1,plain,
( state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o)))))
<=> state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state) ).
tff(3,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
refl(( ( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) )
<=> ( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) )
<=> ! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) )
<=> ! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ004-0.ax',v3_down) ).
tff(8,plain,
! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) )
| ~ state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o)))))
| state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))) )
<=> ( ~ ! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) )
| ~ state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o)))))
| state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) )
| ~ state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o)))))
| state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [B: $i,S3: $i,S2: $i,Y: $i,V1: $i,S1: $i,S4: $i,H: $i,X: $i,V2: $i,E2: $i,V4: $i] :
( ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2)
| state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2) )
| ~ state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o)))))
| state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] :
refl(( ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2)
<=> ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2)
<=> ! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2)
<=> ! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_state) ).
tff(19,plain,
! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [B: $i,S3: $i,S2: $i,V1: $i,E1: $i,S1: $i,S4: $i,H: $i,V2: $i,E2: $i,V4: $i] : ~ state(B,V1,V2,v3(s(s(s(o))),o),V4,H,S1,S2,S3,S4,E1,E2)
| ~ state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ038-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:42:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.39 % SZS status Unsatisfiable
% 0.11/0.39 % SZS output start Proof
% See solution above
% 0.11/0.41 % E exiting
%------------------------------------------------------------------------------