%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN160-1 : 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 05:38:23 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 54
% Syntax : Number of formulae : 117 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 539 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 753 ( 351 ~; 346 |; 0 &)
% ( 56 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 20 ( 20 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 229 ( 209 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
tff(q3_type,type,
q3: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(n3_type,type,
n3: $i > $o ).
tff(b_type,type,
b: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(r4_type,type,
r4: $i > $o ).
tff(n5_type,type,
n5: ( $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(1,plain,
^ [I: $i] :
refl(( ( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ( q2(I,I,I)
| ~ p1(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_181) ).
tff(5,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(10,plain,
k0(e),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(13,plain,
r0(e),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[17,15]) ).
tff(19,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(20,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[20,14]) ).
tff(22,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[22,14]) ).
tff(24,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[23,14]) ).
tff(25,plain,
p1(e,e,e),
inference(unit_resolution,[status(thm)],[24,13,10]) ).
tff(26,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
q2(e,e,e),
inference(unit_resolution,[status(thm)],[31,25,7]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,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(37,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)],[36]) ).
tff(38,axiom,
! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_255) ).
tff(39,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
n0(e,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(45,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
q3(e,e),
inference(unit_resolution,[status(thm)],[51,45,42,32]) ).
tff(53,plain,
^ [A: $i] :
refl(( ( p2(A,A,A)
| ~ q1(A,A,A) )
<=> ( p2(A,A,A)
| ~ q1(A,A,A) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) )
<=> ! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) )
<=> ! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_154) ).
tff(57,plain,
! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
r0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(62,plain,
r0(b),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( ( ~ r0(b)
| q1(b,b,b) )
<=> ( ~ r0(b)
| q1(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( q1(b,b,b)
| ~ r0(b) )
<=> ( ~ r0(b)
| q1(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
( q1(b,b,b)
| ~ r0(b) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_120) ).
tff(66,plain,
( ~ r0(b)
| q1(b,b,b) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ r0(b)
| q1(b,b,b) ),
inference(modus_ponens,[status(thm)],[66,63]) ).
tff(68,plain,
q1(b,b,b),
inference(unit_resolution,[status(thm)],[67,62]) ).
tff(69,plain,
( ( ~ ! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) )
| p2(b,b,b)
| ~ q1(b,b,b) )
<=> ( ~ ! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) )
| p2(b,b,b)
| ~ q1(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) )
| p2(b,b,b)
| ~ q1(b,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [A: $i] :
( p2(A,A,A)
| ~ q1(A,A,A) )
| p2(b,b,b)
| ~ q1(b,b,b) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
p2(b,b,b),
inference(unit_resolution,[status(thm)],[71,68,59]) ).
tff(73,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(74,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)],[73]) ).
tff(75,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(76,axiom,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_240) ).
tff(77,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(b)
| ~ p2(b,b,b) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(b)
| ~ p2(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(b)
| ~ p2(b,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(b)
| ~ p2(b,b,b) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
n3(b),
inference(unit_resolution,[status(thm)],[82,79,72]) ).
tff(84,plain,
( ~ n5(b,b)
<=> ~ n5(b,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
~ n5(b,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(86,plain,
~ n5(b,b),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
^ [B: $i] :
refl(( ( n5(B,B)
| ~ r4(B) )
<=> ( n5(B,B)
| ~ r4(B) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
<=> ! [B: $i] :
( n5(B,B)
| ~ r4(B) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
<=> ! [B: $i] :
( n5(B,B)
| ~ r4(B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
! [B: $i] :
( n5(B,B)
| ~ r4(B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_314) ).
tff(91,plain,
! [B: $i] :
( n5(B,B)
| ~ r4(B) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [B: $i] :
( n5(B,B)
| ~ r4(B) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [B: $i] :
( n5(B,B)
| ~ r4(B) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ( ~ ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
| n5(b,b)
| ~ r4(b) )
<=> ( ~ ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
| n5(b,b)
| ~ r4(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
| n5(b,b)
| ~ r4(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
| n5(b,b)
| ~ r4(b) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
~ r4(b),
inference(unit_resolution,[status(thm)],[96,93,86]) ).
tff(98,plain,
^ [I: $i,J: $i,H: $i,G: $i] :
refl(( ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
^ [I: $i,J: $i,H: $i,G: $i] :
trans(monotonicity(rewrite(( ( r4(G)
| ~ n3(G)
| ~ q3(H,I) )
<=> ( ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
( ( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ( ~ n3(G)
| ~ q3(H,I)
| r4(G)
| ~ p0(J,G) ) )),
rewrite(( ( ~ n3(G)
| ~ q3(H,I)
| r4(G)
| ~ p0(J,G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
( ( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [I: $i,J: $i,H: $i,G: $i] :
( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_298) ).
tff(104,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
p0(c,b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(110,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(c,b)
| r4(b)
| ~ q3(e,e)
| ~ n3(b) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(c,b)
| r4(b)
| ~ q3(e,e)
| ~ n3(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ( ~ p0(c,b)
| ~ n3(b)
| ~ q3(e,e)
| r4(b) )
<=> ( ~ p0(c,b)
| r4(b)
| ~ q3(e,e)
| ~ n3(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(c,b)
| ~ n3(b)
| ~ q3(e,e)
| r4(b) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(c,b)
| r4(b)
| ~ q3(e,e)
| ~ n3(b) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(c,b)
| ~ n3(b)
| ~ q3(e,e)
| r4(b) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(c,b)
| r4(b)
| ~ q3(e,e)
| ~ n3(b) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(c,b)
| ~ n3(b)
| ~ q3(e,e)
| r4(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(c,b)
| r4(b)
| ~ q3(e,e)
| ~ n3(b) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
$false,
inference(unit_resolution,[status(thm)],[116,110,107,97,83,52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN160-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.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 12:29:12 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------