%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN170-1 : 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 05:38:24 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 57 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 221 ( 105 ~; 93 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 114 ( 104 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
tff(p4_type,type,
p4: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(k3_type,type,
k3: ( $i * $i * $i ) > $o ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(1,plain,
^ [B: $i,C: $i] :
refl(( ( p4(B,C,B)
| ~ k3(B,B,C) )
<=> ( p4(B,C,B)
| ~ k3(B,B,C) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
<=> ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
<=> ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_287) ).
tff(5,plain,
! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
^ [D: $i,E: $i] :
refl(( ( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ( p2(D,E,D)
| ~ m1(E,D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(12,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( l0(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(17,plain,
l0(c),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ l0(c)
| m1(c,c,c) )
<=> ( ~ l0(c)
| m1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( m1(c,c,c)
| ~ l0(c) )
<=> ( ~ l0(c)
| m1(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
( m1(c,c,c)
| ~ l0(c) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_020) ).
tff(21,plain,
( ~ l0(c)
| m1(c,c,c) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ l0(c)
| m1(c,c,c) ),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
m1(c,c,c),
inference(unit_resolution,[status(thm)],[22,17]) ).
tff(24,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
p2(c,c,c),
inference(unit_resolution,[status(thm)],[29,23,14]) ).
tff(31,plain,
^ [D: $i,C: $i] :
refl(( ( ~ p2(D,C,C)
| k3(C,D,C) )
<=> ( ~ p2(D,C,C)
| k3(C,D,C) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
<=> ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
<=> ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [D: $i,C: $i] :
rewrite(( ( k3(C,D,C)
| ~ p2(D,C,C) )
<=> ( ~ p2(D,C,C)
| k3(C,D,C) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [D: $i,C: $i] :
( k3(C,D,C)
| ~ p2(D,C,C) )
<=> ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [D: $i,C: $i] :
( k3(C,D,C)
| ~ p2(D,C,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_206) ).
tff(37,plain,
! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
| ~ p2(c,c,c)
| k3(c,c,c) )
<=> ( ~ ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
| ~ p2(c,c,c)
| k3(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
| ~ p2(c,c,c)
| k3(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [D: $i,C: $i] :
( ~ p2(D,C,C)
| k3(C,D,C) )
| ~ p2(c,c,c)
| k3(c,c,c) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
k3(c,c,c),
inference(unit_resolution,[status(thm)],[43,40,30]) ).
tff(45,plain,
( ( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| p4(c,c,c)
| ~ k3(c,c,c) )
<=> ( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| p4(c,c,c)
| ~ k3(c,c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| p4(c,c,c)
| ~ k3(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| p4(c,c,c)
| ~ k3(c,c,c) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
p4(c,c,c),
inference(unit_resolution,[status(thm)],[47,44,7]) ).
tff(49,plain,
^ [Y: $i,X: $i] :
refl(( ~ p4(X,c,Y)
<=> ~ p4(X,c,Y) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [Y: $i,X: $i] : ~ p4(X,c,Y)
<=> ! [Y: $i,X: $i] : ~ p4(X,c,Y) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [Y: $i,X: $i] : ~ p4(X,c,Y)
<=> ! [Y: $i,X: $i] : ~ p4(X,c,Y) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [Y: $i,X: $i] : ~ p4(X,c,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(53,plain,
! [Y: $i,X: $i] : ~ p4(X,c,Y),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [Y: $i,X: $i] : ~ p4(X,c,Y),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [Y: $i,X: $i] : ~ p4(X,c,Y),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ~ p4(X,c,Y)
| ~ p4(c,c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,55,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN170-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:29:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47 % SZS output start Proof
% See solution above
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------