%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN183-1 : 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 05:38:26 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 79
% Syntax : Number of formulae : 182 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 931 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1324 ( 618 ~; 613 |; 0 &)
% ( 93 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 43 ( 43 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 343 ( 313 !; 0 ?; 343 :)
% Comments :
%------------------------------------------------------------------------------
tff(m3_type,type,
m3: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(n2_type,type,
n2: $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(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(q4_type,type,
q4: ( $i * $i ) > $o ).
tff(q5_type,type,
q5: ( $i * $i ) > $o ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(k3_type,type,
k3: ( $i * $i * $i ) > $o ).
tff(r1_type,type,
r1: $i > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(s0_type,type,
s0: $i > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( n2(A)
| ~ p1(B,C,A) )
<=> ( n2(A)
| ~ p1(B,C,A) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
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/sandbox/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/sandbox/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/sandbox/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,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
n2(e),
inference(unit_resolution,[status(thm)],[28,25,7]) ).
tff(30,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(31,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)],[30]) ).
tff(32,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(33,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(34,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(40,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
m1(e,e,e),
inference(unit_resolution,[status(thm)],[41,13]) ).
tff(43,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(44,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,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)],[44]) ).
tff(46,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)],[45,43]) ).
tff(47,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(48,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)],[47,46]) ).
tff(49,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[48,42,36]) ).
tff(50,plain,
^ [D: $i] :
refl(( ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
^ [D: $i] :
trans(monotonicity(rewrite(( ( m3(D,e,e)
| ~ n2(e) )
<=> ( ~ n2(e)
| m3(D,e,e) ) )),
( ( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| m3(D,e,e)
| ~ p2(D,e,e) ) )),
rewrite(( ( ~ n2(e)
| m3(D,e,e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
( ( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [D: $i] :
( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [D: $i] :
( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_234) ).
tff(56,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) )
<=> ( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
m3(e,e,e),
inference(unit_resolution,[status(thm)],[62,59,49,29]) ).
tff(64,plain,
( ~ q5(e,e)
<=> ~ q5(e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
~ q5(e,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(66,plain,
~ q5(e,e),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
^ [H: $i] :
refl(( ( q5(H,H)
| ~ q4(H,H) )
<=> ( q5(H,H)
| ~ q4(H,H) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
<=> ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
<=> ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_325) ).
tff(71,plain,
! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ( ~ ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
| q5(e,e)
| ~ q4(e,e) )
<=> ( ~ ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
| q5(e,e)
| ~ q4(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
| q5(e,e)
| ~ q4(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
| q5(e,e)
| ~ q4(e,e) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ q4(e,e),
inference(unit_resolution,[status(thm)],[76,73,66]) ).
tff(78,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(79,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)],[78]) ).
tff(80,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(81,axiom,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_181) ).
tff(82,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,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(86,plain,
( ( q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,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)],[86]) ).
tff(88,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)],[87,85]) ).
tff(89,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(90,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
q2(e,e,e),
inference(unit_resolution,[status(thm)],[90,25,84]) ).
tff(92,plain,
^ [I: $i,A: $i,J: $i] :
refl(( ( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
<=> ( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
^ [I: $i,A: $i,J: $i] :
trans(monotonicity(rewrite(( ( k3(I,I,I)
| ~ r1(I) )
<=> ( ~ r1(I)
| k3(I,I,I) ) )),
( ( k3(I,I,I)
| ~ r1(I)
| ~ p2(J,A,A) )
<=> ( ~ r1(I)
| k3(I,I,I)
| ~ p2(J,A,A) ) )),
rewrite(( ( ~ r1(I)
| k3(I,I,I)
| ~ p2(J,A,A) )
<=> ( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) )),
( ( k3(I,I,I)
| ~ r1(I)
| ~ p2(J,A,A) )
<=> ( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [I: $i,A: $i,J: $i] :
( k3(I,I,I)
| ~ r1(I)
| ~ p2(J,A,A) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [I: $i,A: $i,J: $i] :
( k3(I,I,I)
| ~ r1(I)
| ~ p2(J,A,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_213) ).
tff(98,plain,
! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
^ [D: $i,E: $i] :
refl(( ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
^ [D: $i,E: $i] :
trans(monotonicity(rewrite(( ( r1(D)
| ~ q0(D,E)
| ~ s0(d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| r1(D) ) )),
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| r1(D)
| ~ q1(d,E,d) ) )),
rewrite(( ( ~ q0(D,E)
| ~ s0(d)
| r1(D)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [D: $i,E: $i] :
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,axiom,
! [D: $i,E: $i] :
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_124) ).
tff(108,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
( s0(d)
<=> s0(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(114,plain,
s0(d),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ( q1(d,d,d)
| ~ k0(e) )
<=> ( ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,axiom,
( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_117) ).
tff(121,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[121,115]) ).
tff(123,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[123,115]) ).
tff(125,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[124,115]) ).
tff(126,plain,
q1(d,d,d),
inference(unit_resolution,[status(thm)],[125,114,10]) ).
tff(127,plain,
( q0(e,d)
<=> q0(e,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,axiom,
q0(e,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_2) ).
tff(129,plain,
q0(e,d),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,plain,
( ( ~ q0(e,d)
| ~ s0(d)
| ~ q1(d,d,d)
| r1(e) )
<=> ( ~ s0(d)
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(e,d)
| ~ s0(d)
| ~ q1(d,d,d)
| r1(e) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ) ),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(e,d)
| ~ s0(d)
| ~ q1(d,d,d)
| r1(e) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ) ),
inference(transitivity,[status(thm)],[132,130]) ).
tff(134,plain,
( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(e,d)
| ~ s0(d)
| ~ q1(d,d,d)
| r1(e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
| ~ s0(d)
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
r1(e),
inference(unit_resolution,[status(thm)],[135,114,129,126,111]) ).
tff(137,plain,
^ [B: $i] :
refl(( ( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ( p2(B,B,B)
| ~ n1(d,d,B) ) )),
inference(bind,[status(th)],[]) ).
tff(138,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_153) ).
tff(141,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(skolemize,[status(sab)],[141]) ).
tff(143,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
( q0(d,d)
<=> q0(d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,axiom,
q0(d,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(146,plain,
q0(d,d),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(149,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[149,147]) ).
tff(151,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[150,147]) ).
tff(152,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[152,147]) ).
tff(154,plain,
n1(d,d,d),
inference(unit_resolution,[status(thm)],[153,146]) ).
tff(155,plain,
( ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) )
<=> ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
p2(d,d,d),
inference(unit_resolution,[status(thm)],[157,154,143]) ).
tff(159,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
( ( ~ p2(d,d,d)
| ~ r1(e)
| k3(e,e,e) )
<=> ( ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ p2(d,d,d)
| ~ r1(e)
| k3(e,e,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ p2(d,d,d)
| ~ r1(e)
| k3(e,e,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ p2(d,d,d)
| ~ r1(e)
| k3(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
k3(e,e,e),
inference(unit_resolution,[status(thm)],[164,158,136,101]) ).
tff(166,plain,
^ [B: $i,D: $i,E: $i,F: $i,C: $i] :
refl(( ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
^ [B: $i,D: $i,E: $i,F: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( q4(B,C)
| ~ k3(D,D,B) )
<=> ( ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B) )
<=> ( ~ k3(D,D,B)
| q4(B,C)
| ~ q2(E,C,B) ) )),
rewrite(( ( ~ k3(D,D,B)
| q4(B,C)
| ~ q2(E,C,B) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C)
| ~ m3(E,F,E) ) )),
rewrite(( ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C)
| ~ m3(E,F,E) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
inference(bind,[status(th)],[]) ).
tff(170,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,axiom,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_295) ).
tff(172,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[172,168]) ).
tff(174,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[174,167]) ).
tff(176,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ( ~ m3(e,e,e)
| ~ q2(e,e,e)
| ~ k3(e,e,e)
| q4(e,e) )
<=> ( ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(e,e,e)
| ~ q2(e,e,e)
| ~ k3(e,e,e)
| q4(e,e) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(e,e,e)
| ~ q2(e,e,e)
| ~ k3(e,e,e)
| q4(e,e) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(e,e,e)
| ~ q2(e,e,e)
| ~ k3(e,e,e)
| q4(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
$false,
inference(unit_resolution,[status(thm)],[181,175,165,91,77,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN183-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.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 12:28:50 EDT 2025
% 0.11/0.32 % 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
%------------------------------------------------------------------------------