%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN148-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:38:21 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.56s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 60 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 387 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 561 ( 264 ~; 259 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 131 ( 117 !; 0 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(d_type,type,
d: $i ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(s0_type,type,
s0: $i > $o ).
tff(1,plain,
^ [H: $i,G: $i] :
refl(( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [H: $i,G: $i] :
rewrite(( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(7,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(13,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,c)
| l1(c,c) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,c)
| l1(c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,c)
| l1(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,c)
| l1(c,c) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
l1(c,c),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
( ~ n1(c,d,d)
<=> ~ n1(c,d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
~ n1(c,d,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(20,plain,
~ n1(c,d,d),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [E: $i,F: $i,G: $i] :
refl(( ( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
<=> ( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
<=> ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
<=> ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [E: $i,F: $i,G: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( n1(E,F,F)
| ~ l0(G) )
<=> ( ~ l0(G)
| n1(E,F,F) ) )),
( ( n1(E,F,F)
| ~ l0(G)
| ~ l1(G,E) )
<=> ( ~ l0(G)
| n1(E,F,F)
| ~ l1(G,E) ) )),
rewrite(( ( ~ l0(G)
| n1(E,F,F)
| ~ l1(G,E) )
<=> ( ~ l0(G)
| ~ l1(G,E)
| n1(E,F,F) ) )),
( ( n1(E,F,F)
| ~ l0(G)
| ~ l1(G,E) )
<=> ( ~ l0(G)
| ~ l1(G,E)
| n1(E,F,F) ) )),
( ( n1(E,F,F)
| ~ l0(G)
| ~ l1(G,E)
| ~ n1(E,F,E) )
<=> ( ~ l0(G)
| ~ l1(G,E)
| n1(E,F,F)
| ~ n1(E,F,E) ) )),
rewrite(( ( ~ l0(G)
| ~ l1(G,E)
| n1(E,F,F)
| ~ n1(E,F,E) )
<=> ( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ) )),
( ( n1(E,F,F)
| ~ l0(G)
| ~ l1(G,E)
| ~ n1(E,F,E) )
<=> ( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [E: $i,F: $i,G: $i] :
( n1(E,F,F)
| ~ l0(G)
| ~ l1(G,E)
| ~ n1(E,F,E) )
<=> ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [E: $i,F: $i,G: $i] :
( n1(E,F,F)
| ~ l0(G)
| ~ l1(G,E)
| ~ n1(E,F,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_054) ).
tff(27,plain,
! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( l0(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(33,plain,
l0(c),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ( ~ ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
| ~ l0(c)
| ~ l1(c,c)
| n1(c,d,d)
| ~ n1(c,d,c) )
<=> ( ~ ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
| ~ l0(c)
| ~ l1(c,c)
| n1(c,d,d)
| ~ n1(c,d,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ l0(c)
| ~ n1(c,d,c)
| ~ l1(c,c)
| n1(c,d,d) )
<=> ( ~ l0(c)
| ~ l1(c,c)
| n1(c,d,d)
| ~ n1(c,d,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
| ~ l0(c)
| ~ n1(c,d,c)
| ~ l1(c,c)
| n1(c,d,d) )
<=> ( ~ ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
| ~ l0(c)
| ~ l1(c,c)
| n1(c,d,d)
| ~ n1(c,d,c) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
| ~ l0(c)
| ~ n1(c,d,c)
| ~ l1(c,c)
| n1(c,d,d) )
<=> ( ~ ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
| ~ l0(c)
| ~ l1(c,c)
| n1(c,d,d)
| ~ n1(c,d,c) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
| ~ l0(c)
| ~ n1(c,d,c)
| ~ l1(c,c)
| n1(c,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [E: $i,F: $i,G: $i] :
( ~ l0(G)
| ~ n1(E,F,E)
| ~ l1(G,E)
| n1(E,F,F) )
| ~ l0(c)
| ~ l1(c,c)
| n1(c,d,d)
| ~ n1(c,d,c) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ n1(c,d,c),
inference(unit_resolution,[status(thm)],[39,33,30,20,17]) ).
tff(41,plain,
^ [D: $i,E: $i] :
refl(( ( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) )
<=> ( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) )
<=> ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) )
<=> ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [D: $i,E: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( n1(D,E,D)
| ~ s0(b) )
<=> ( ~ s0(b)
| n1(D,E,D) ) )),
( ( n1(D,E,D)
| ~ s0(b)
| ~ l0(D) )
<=> ( ~ s0(b)
| n1(D,E,D)
| ~ l0(D) ) )),
rewrite(( ( ~ s0(b)
| n1(D,E,D)
| ~ l0(D) )
<=> ( ~ l0(D)
| ~ s0(b)
| n1(D,E,D) ) )),
( ( n1(D,E,D)
| ~ s0(b)
| ~ l0(D) )
<=> ( ~ l0(D)
| ~ s0(b)
| n1(D,E,D) ) )),
( ( n1(D,E,D)
| ~ s0(b)
| ~ l0(D)
| ~ p0(b,E) )
<=> ( ~ l0(D)
| ~ s0(b)
| n1(D,E,D)
| ~ p0(b,E) ) )),
rewrite(( ( ~ l0(D)
| ~ s0(b)
| n1(D,E,D)
| ~ p0(b,E) )
<=> ( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ) )),
( ( n1(D,E,D)
| ~ s0(b)
| ~ l0(D)
| ~ p0(b,E) )
<=> ( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [D: $i,E: $i] :
( n1(D,E,D)
| ~ s0(b)
| ~ l0(D)
| ~ p0(b,E) )
<=> ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [D: $i,E: $i] :
( n1(D,E,D)
| ~ s0(b)
| ~ l0(D)
| ~ p0(b,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_050) ).
tff(47,plain,
! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(53,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( s0(b)
<=> s0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
s0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_5) ).
tff(56,plain,
s0(b),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) )
| ~ l0(c)
| ~ s0(b)
| ~ p0(b,d)
| n1(c,d,c) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) )
| ~ l0(c)
| ~ s0(b)
| ~ p0(b,d)
| n1(c,d,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) )
| ~ l0(c)
| ~ s0(b)
| ~ p0(b,d)
| n1(c,d,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [D: $i,E: $i] :
( ~ l0(D)
| ~ s0(b)
| ~ p0(b,E)
| n1(D,E,D) )
| ~ l0(c)
| ~ s0(b)
| ~ p0(b,d)
| n1(c,d,c) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,56,53,33,50,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN148-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n008.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 12:29:03 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.56 % SZS status Unsatisfiable
% 0.18/0.56 % SZS output start Proof
% See solution above
% 0.18/0.57 % E exiting
%------------------------------------------------------------------------------