%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN217-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:38:31 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 50 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 298 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 426 ( 201 ~; 195 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 124 ( 111 !; 0 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(a_type,type,
a: $i ).
tff(l2_type,type,
l2: ( $i * $i ) > $o ).
tff(1,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [B: $i,D: $i,C: $i] :
trans(monotonicity(rewrite(( ( m1(B,C,C)
| ~ l0(D) )
<=> ( ~ l0(D)
| m1(B,C,C) ) )),
( ( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| m1(B,C,C)
| ~ m0(C,C,B) ) )),
rewrite(( ( ~ l0(D)
| m1(B,C,C)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
( ( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,D: $i,C: $i] :
( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [B: $i,D: $i,C: $i] :
( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_015) ).
tff(7,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( m0(b,b,e)
<=> m0(b,b,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
m0(b,b,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_31) ).
tff(13,plain,
m0(b,b,e),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(16,plain,
l0(a),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(b,b,e)
| m1(e,b,b) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(b,b,e)
| m1(e,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(b,b,e)
| m1(e,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(b,b,e)
| m1(e,b,b) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
m1(e,b,b),
inference(unit_resolution,[status(thm)],[19,16,13,10]) ).
tff(21,plain,
( ~ l2(b,b)
<=> ~ l2(b,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
~ l2(b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(23,plain,
~ l2(b,b),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [I: $i,H: $i,G: $i] :
refl(( ( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
<=> ( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [I: $i,H: $i,G: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( l2(G,G)
| ~ m0(H,G,I) )
<=> ( ~ m0(H,G,I)
| l2(G,G) ) )),
( ( l2(G,G)
| ~ m0(H,G,I)
| ~ m1(I,H,H) )
<=> ( ~ m0(H,G,I)
| l2(G,G)
| ~ m1(I,H,H) ) )),
rewrite(( ( ~ m0(H,G,I)
| l2(G,G)
| ~ m1(I,H,H) )
<=> ( ~ m0(H,G,I)
| l2(G,G)
| ~ m1(I,H,H) ) )),
( ( l2(G,G)
| ~ m0(H,G,I)
| ~ m1(I,H,H) )
<=> ( ~ m0(H,G,I)
| l2(G,G)
| ~ m1(I,H,H) ) )),
( ( l2(G,G)
| ~ m0(H,G,I)
| ~ m1(I,H,H)
| ~ p0(H,G) )
<=> ( ~ m0(H,G,I)
| l2(G,G)
| ~ m1(I,H,H)
| ~ p0(H,G) ) )),
rewrite(( ( ~ m0(H,G,I)
| l2(G,G)
| ~ m1(I,H,H)
| ~ p0(H,G) )
<=> ( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ) )),
( ( l2(G,G)
| ~ m0(H,G,I)
| ~ m1(I,H,H)
| ~ p0(H,G) )
<=> ( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [I: $i,H: $i,G: $i] :
( l2(G,G)
| ~ m0(H,G,I)
| ~ m1(I,H,H)
| ~ p0(H,G) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [I: $i,H: $i,G: $i] :
( l2(G,G)
| ~ m0(H,G,I)
| ~ m1(I,H,H)
| ~ p0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_134) ).
tff(30,plain,
! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
| l2(b,b)
| ~ m0(b,b,e)
| ~ p0(b,b)
| ~ m1(e,b,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
| l2(b,b)
| ~ m0(b,b,e)
| ~ p0(b,b)
| ~ m1(e,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ m0(b,b,e)
| ~ p0(b,b)
| l2(b,b)
| ~ m1(e,b,b) )
<=> ( l2(b,b)
| ~ m0(b,b,e)
| ~ p0(b,b)
| ~ m1(e,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
| ~ m0(b,b,e)
| ~ p0(b,b)
| l2(b,b)
| ~ m1(e,b,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
| l2(b,b)
| ~ m0(b,b,e)
| ~ p0(b,b)
| ~ m1(e,b,b) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
| ~ m0(b,b,e)
| ~ p0(b,b)
| l2(b,b)
| ~ m1(e,b,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
| l2(b,b)
| ~ m0(b,b,e)
| ~ p0(b,b)
| ~ m1(e,b,b) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
| ~ m0(b,b,e)
| ~ p0(b,b)
| l2(b,b)
| ~ m1(e,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ m0(H,G,I)
| ~ p0(H,G)
| l2(G,G)
| ~ m1(I,H,H) )
| l2(b,b)
| ~ m0(b,b,e)
| ~ p0(b,b)
| ~ m1(e,b,b) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ p0(b,b)
| ~ m1(e,b,b) ),
inference(unit_resolution,[status(thm)],[39,13,33,23]) ).
tff(41,plain,
~ p0(b,b),
inference(unit_resolution,[status(thm)],[40,20]) ).
tff(42,plain,
^ [X: $i] :
refl(( p0(b,X)
<=> p0(b,X) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [X: $i] : p0(b,X)
<=> ! [X: $i] : p0(b,X) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X: $i] : p0(b,X)
<=> ! [X: $i] : p0(b,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [X: $i] : p0(b,X),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_14) ).
tff(46,plain,
! [X: $i] : p0(b,X),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i] : p0(b,X),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X: $i] : p0(b,X),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [X: $i] : p0(b,X)
| p0(b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,48,41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN217-1 : TPTP v9.0.0. Released v1.1.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.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 12:31:02 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.44 % SZS status Unsatisfiable
% 0.18/0.44 % SZS output start Proof
% See solution above
% 0.18/0.46 % E exiting
%------------------------------------------------------------------------------