%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN134-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:19 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.45s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 49 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 301 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 447 ( 211 ~; 207 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 147 ( 133 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(b_type,type,
b: $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(m2_type,type,
m2: $i > $o ).
tff(d_type,type,
d: $i ).
tff(s0_type,type,
s0: $i > $o ).
tff(1,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
refl(( ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( l1(C,D)
| ~ p0(E,C) )
<=> ( ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F) )
<=> ( ~ p0(E,C)
| l1(C,D)
| ~ r0(F) ) )),
rewrite(( ( ~ p0(E,C)
| l1(C,D)
| ~ r0(F) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D)
| ~ m0(D,C,E) ) )),
rewrite(( ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D)
| ~ m0(D,C,E) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [D: $i,E: $i,F: $i,C: $i] :
( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_003) ).
tff(7,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
m0(e,b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(13,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(16,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(19,plain,
r0(b),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
l1(b,e),
inference(unit_resolution,[status(thm)],[25,19,16,13,10]) ).
tff(27,plain,
( ~ m2(d)
<=> ~ m2(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
~ m2(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(29,plain,
~ m2(d),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [H: $i,F: $i,G: $i] :
refl(( ( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
<=> ( ~ s0(F)
| ~ l1(G,H)
| m2(F) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
<=> ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
<=> ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [H: $i,F: $i,G: $i] :
rewrite(( ( m2(F)
| ~ s0(F)
| ~ l1(G,H) )
<=> ( ~ s0(F)
| ~ l1(G,H)
| m2(F) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [H: $i,F: $i,G: $i] :
( m2(F)
| ~ s0(F)
| ~ l1(G,H) )
<=> ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [H: $i,F: $i,G: $i] :
( m2(F)
| ~ s0(F)
| ~ l1(G,H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_135) ).
tff(36,plain,
! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( s0(d)
<=> s0(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(42,plain,
s0(d),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
( ( ~ ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
| ~ s0(d)
| m2(d)
| ~ l1(b,e) )
<=> ( ~ ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
| ~ s0(d)
| m2(d)
| ~ l1(b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ s0(d)
| ~ l1(b,e)
| m2(d) )
<=> ( ~ s0(d)
| m2(d)
| ~ l1(b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
| ~ s0(d)
| ~ l1(b,e)
| m2(d) )
<=> ( ~ ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
| ~ s0(d)
| m2(d)
| ~ l1(b,e) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
| ~ s0(d)
| ~ l1(b,e)
| m2(d) )
<=> ( ~ ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
| ~ s0(d)
| m2(d)
| ~ l1(b,e) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
| ~ s0(d)
| ~ l1(b,e)
| m2(d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [H: $i,F: $i,G: $i] :
( ~ s0(F)
| ~ l1(G,H)
| m2(F) )
| ~ s0(d)
| m2(d)
| ~ l1(b,e) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,42,39,29,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN134-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.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 : Fri Jun 20 12:28:42 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.45 % SZS status Unsatisfiable
% 0.18/0.45 % SZS output start Proof
% See solution above
% 0.18/0.46 % E exiting
%------------------------------------------------------------------------------