%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN262-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:37 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 43 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 228 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 318 ( 149 ~; 144 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 118 ( 106 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(b_type,type,
b: $i ).
tff(c_type,type,
c: $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(k0_type,type,
k0: $i > $o ).
tff(1,plain,
( ~ p1(b,c,b)
<=> ~ p1(b,c,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ p1(b,c,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(3,plain,
~ p1(b,c,b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
refl(( ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(monotonicity(rewrite(( ( p1(H,I,J)
| ~ m0(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J) ) )),
( ( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
rewrite(( ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
( ( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [I: $i,A: $i,J: $i,H: $i] :
( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_082) ).
tff(10,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( m0(b,b,e)
<=> m0(b,b,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
m0(b,b,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_31) ).
tff(16,plain,
m0(b,b,e),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,c,b)
| ~ m0(b,b,e)
| ~ p1(b,b,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,c,b)
| ~ m0(b,b,e)
| ~ p1(b,b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ m0(b,b,e)
| p1(b,c,b)
| ~ p1(b,b,e) )
<=> ( p1(b,c,b)
| ~ m0(b,b,e)
| ~ p1(b,b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,b,e)
| p1(b,c,b)
| ~ p1(b,b,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,c,b)
| ~ m0(b,b,e)
| ~ p1(b,b,e) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,b,e)
| p1(b,c,b)
| ~ p1(b,b,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,c,b)
| ~ m0(b,b,e)
| ~ p1(b,b,e) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| ~ m0(b,b,e)
| p1(b,c,b)
| ~ p1(b,b,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ m0(J,H,A)
| p1(H,I,J)
| ~ p1(J,H,A) )
| p1(b,c,b)
| ~ m0(b,b,e)
| ~ p1(b,b,e) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ p1(b,b,e),
inference(unit_resolution,[status(thm)],[22,16,13,3]) ).
tff(24,plain,
^ [D: $i,E: $i] :
refl(( ( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
<=> ( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
<=> ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
<=> ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [D: $i,E: $i] :
trans(monotonicity(rewrite(( ( p1(D,D,E)
| ~ n0(d,D) )
<=> ( ~ n0(d,D)
| p1(D,D,E) ) )),
( ( p1(D,D,E)
| ~ n0(d,D)
| ~ k0(E) )
<=> ( ~ n0(d,D)
| p1(D,D,E)
| ~ k0(E) ) )),
rewrite(( ( ~ n0(d,D)
| p1(D,D,E)
| ~ k0(E) )
<=> ( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) )),
( ( p1(D,D,E)
| ~ n0(d,D)
| ~ k0(E) )
<=> ( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [D: $i,E: $i] :
( p1(D,D,E)
| ~ n0(d,D)
| ~ k0(E) )
<=> ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [D: $i,E: $i] :
( p1(D,D,E)
| ~ n0(d,D)
| ~ k0(E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_063) ).
tff(30,plain,
! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(36,plain,
k0(e),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( n0(d,b)
<=> n0(d,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
n0(d,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_7) ).
tff(39,plain,
n0(d,b),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
| ~ k0(e)
| ~ n0(d,b)
| p1(b,b,e) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
| ~ k0(e)
| ~ n0(d,b)
| p1(b,b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
| ~ k0(e)
| ~ n0(d,b)
| p1(b,b,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
| ~ k0(e)
| ~ n0(d,b)
| p1(b,b,e) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
$false,
inference(unit_resolution,[status(thm)],[42,39,36,33,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN262-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:31:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% See solution above
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------