%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN141-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:38:20 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 59
% Syntax : Number of formulae : 130 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 602 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 836 ( 392 ~; 380 |; 0 &)
% ( 64 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 277 ( 252 !; 0 ?; 277 :)
% Comments :
%------------------------------------------------------------------------------
tff(m5_type,type,
m5: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(k4_type,type,
k4: $i > $o ).
tff(n3_type,type,
n3: $i > $o ).
tff(e_type,type,
e: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(q3_type,type,
q3: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(1,plain,
^ [C: $i] :
refl(( ( m5(C,C)
| ~ k4(C) )
<=> ( m5(C,C)
| ~ k4(C) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [C: $i] :
( m5(C,C)
| ~ k4(C) )
<=> ! [C: $i] :
( m5(C,C)
| ~ k4(C) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [C: $i] :
( m5(C,C)
| ~ k4(C) )
<=> ! [C: $i] :
( m5(C,C)
| ~ k4(C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [C: $i] :
( m5(C,C)
| ~ k4(C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_304) ).
tff(5,plain,
! [C: $i] :
( m5(C,C)
| ~ k4(C) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [C: $i] :
( m5(C,C)
| ~ k4(C) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [C: $i] :
( m5(C,C)
| ~ k4(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,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(17,plain,
r0(e),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(21,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
m1(e,e,e),
inference(unit_resolution,[status(thm)],[22,17]) ).
tff(24,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[29,23,14]) ).
tff(31,plain,
^ [D: $i,E: $i,F: $i] :
refl(( ( n3(D)
| ~ p2(E,F,D) )
<=> ( n3(D)
| ~ p2(E,F,D) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
<=> ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
<=> ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_240) ).
tff(35,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
n3(e),
inference(unit_resolution,[status(thm)],[40,37,30]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,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(46,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)],[45]) ).
tff(47,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(48,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)],[47,46]) ).
tff(49,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)],[48,44]) ).
tff(50,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)],[49]) ).
tff(51,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)],[50,43]) ).
tff(52,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
m0(e,b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(54,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(57,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(60,plain,
r0(b),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,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(62,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(63,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)],[62]) ).
tff(64,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)],[63,61]) ).
tff(65,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(66,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)],[65,64]) ).
tff(67,plain,
l1(b,e),
inference(unit_resolution,[status(thm)],[66,60,57,54,51]) ).
tff(68,plain,
^ [H: $i,G: $i] :
refl(( ( ~ l1(H,G)
| q2(G,G,H) )
<=> ( ~ l1(H,G)
| q2(G,G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [H: $i,G: $i] :
rewrite(( ( q2(G,G,H)
| ~ l1(H,G) )
<=> ( ~ l1(H,G)
| q2(G,G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_186) ).
tff(74,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
q2(e,e,b),
inference(unit_resolution,[status(thm)],[80,77,67]) ).
tff(82,plain,
^ [I: $i,H: $i,G: $i] :
refl(( ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [I: $i,H: $i,G: $i] :
trans(monotonicity(rewrite(( ( q3(G,H)
| ~ q2(I,G,H) )
<=> ( ~ q2(I,G,H)
| q3(G,H) ) )),
( ( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| q3(G,H)
| ~ n0(I,G) ) )),
rewrite(( ( ~ q2(I,G,H)
| q3(G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
( ( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_255) ).
tff(88,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
n0(e,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(94,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
q3(e,b),
inference(unit_resolution,[status(thm)],[100,94,91,81]) ).
tff(102,plain,
( n0(c,d)
<=> n0(c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
n0(c,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
tff(104,plain,
n0(c,d),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ( k4(c)
| ~ n0(c,d)
| ~ q3(e,b) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,axiom,
( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_274) ).
tff(111,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[111,105]) ).
tff(113,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[112,105]) ).
tff(114,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[113,105]) ).
tff(115,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[114,105]) ).
tff(116,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(unit_resolution,[status(thm)],[115,104]) ).
tff(117,plain,
k4(c),
inference(unit_resolution,[status(thm)],[116,101,41]) ).
tff(118,plain,
( ( ~ ! [C: $i] :
( m5(C,C)
| ~ k4(C) )
| m5(c,c)
| ~ k4(c) )
<=> ( ~ ! [C: $i] :
( m5(C,C)
| ~ k4(C) )
| m5(c,c)
| ~ k4(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [C: $i] :
( m5(C,C)
| ~ k4(C) )
| m5(c,c)
| ~ k4(c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [C: $i] :
( m5(C,C)
| ~ k4(C) )
| m5(c,c)
| ~ k4(c) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
m5(c,c),
inference(unit_resolution,[status(thm)],[120,117,7]) ).
tff(122,plain,
^ [X: $i] :
refl(( ~ m5(c,X)
<=> ~ m5(c,X) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [X: $i] : ~ m5(c,X)
<=> ! [X: $i] : ~ m5(c,X) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [X: $i] : ~ m5(c,X)
<=> ! [X: $i] : ~ m5(c,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
! [X: $i] : ~ m5(c,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(126,plain,
! [X: $i] : ~ m5(c,X),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [X: $i] : ~ m5(c,X),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [X: $i] : ~ m5(c,X),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
( ~ ! [X: $i] : ~ m5(c,X)
| ~ m5(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
$false,
inference(unit_resolution,[status(thm)],[129,128,121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN141-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:27:40 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47 % SZS output start Proof
% See solution above
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------