%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN194-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:38:28 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 58
% Syntax : Number of formulae : 127 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 603 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 838 ( 390 ~; 384 |; 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 : 271 ( 246 !; 0 ?; 271 :)
% Comments :
%------------------------------------------------------------------------------
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(e_type,type,
e: $i ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
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(q3_type,type,
q3: ( $i * $i ) > $o ).
tff(k4_type,type,
k4: $i > $o ).
tff(r5_type,type,
r5: ( $i * $i ) > $o ).
tff(n3_type,type,
n3: $i > $o ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,
^ [H: $i,G: $i] :
refl(( ( ~ l1(H,G)
| q2(G,G,H) )
<=> ( ~ l1(H,G)
| q2(G,G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30]) ).
tff(32,axiom,
! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_186) ).
tff(33,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,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(38,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(39,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
q2(e,e,b),
inference(unit_resolution,[status(thm)],[39,36,26]) ).
tff(41,plain,
( ~ r5(c,c)
<=> ~ r5(c,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
~ r5(c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(43,plain,
~ r5(c,c),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
^ [B: $i] :
refl(( ( ~ k4(B)
| r5(B,B) )
<=> ( ~ k4(B)
| r5(B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [B: $i] :
( ~ k4(B)
| r5(B,B) )
<=> ! [B: $i] :
( ~ k4(B)
| r5(B,B) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [B: $i] :
( ~ k4(B)
| r5(B,B) )
<=> ! [B: $i] :
( ~ k4(B)
| r5(B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [B: $i] :
rewrite(( ( r5(B,B)
| ~ k4(B) )
<=> ( ~ k4(B)
| r5(B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [B: $i] :
( r5(B,B)
| ~ k4(B) )
<=> ! [B: $i] :
( ~ k4(B)
| r5(B,B) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [B: $i] :
( r5(B,B)
| ~ k4(B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_328) ).
tff(50,plain,
! [B: $i] :
( ~ k4(B)
| r5(B,B) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [B: $i] :
( ~ k4(B)
| r5(B,B) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [B: $i] :
( ~ k4(B)
| r5(B,B) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [B: $i] :
( ~ k4(B)
| r5(B,B) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [B: $i] :
( ~ k4(B)
| r5(B,B) )
| ~ k4(c)
| r5(c,c) )
<=> ( ~ ! [B: $i] :
( ~ k4(B)
| r5(B,B) )
| ~ k4(c)
| r5(c,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [B: $i] :
( ~ k4(B)
| r5(B,B) )
| ~ k4(c)
| r5(c,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [B: $i] :
( ~ k4(B)
| r5(B,B) )
| ~ k4(c)
| r5(c,c) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ k4(c),
inference(unit_resolution,[status(thm)],[56,53,43]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(62,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(67,plain,
r0(e),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(71,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[71,68]) ).
tff(73,plain,
m1(e,e,e),
inference(unit_resolution,[status(thm)],[72,67]) ).
tff(74,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(75,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,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)],[75]) ).
tff(77,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)],[76,74]) ).
tff(78,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(79,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)],[78,77]) ).
tff(80,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[79,73,64]) ).
tff(81,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(82,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)],[81]) ).
tff(83,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(84,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(85,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,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(89,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(90,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
n3(e),
inference(unit_resolution,[status(thm)],[90,87,80]) ).
tff(92,plain,
( n0(c,d)
<=> n0(c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
n0(c,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
tff(94,plain,
n0(c,d),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,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(96,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(97,plain,
( ( k4(c)
| ~ n0(c,d)
| ~ q3(e,b) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,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)],[97]) ).
tff(99,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)],[98,96]) ).
tff(100,axiom,
( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_274) ).
tff(101,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[101,95]) ).
tff(103,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[103,95]) ).
tff(105,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[104,95]) ).
tff(106,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(unit_resolution,[status(thm)],[105,94]) ).
tff(107,plain,
~ q3(e,b),
inference(unit_resolution,[status(thm)],[106,91,57]) ).
tff(108,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(109,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)],[108]) ).
tff(110,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(111,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(112,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)],[111]) ).
tff(113,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(114,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
n0(e,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(120,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,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(122,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(123,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)],[122]) ).
tff(124,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)],[123,121]) ).
tff(125,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(126,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)],[125,124]) ).
tff(127,plain,
$false,
inference(unit_resolution,[status(thm)],[126,120,117,107,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN194-1 : TPTP v9.0.0. Released v1.1.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.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 12:28:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% See solution above
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------