%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL192-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 02:59:31 PM UTC 2026
% Result : Unsatisfiable 162.53s 162.80s
% Output : Proof 163.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 69
% Syntax : Number of formulae : 269 ( 208 unt; 0 typ; 0 def)
% Number of atoms : 344 ( 336 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 118 ( 50 ~; 46 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 248 ( 232 !; 0 ?; 248 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(theorem_type,type,
theorem: $i > $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(r_type,type,
r: $i ).
tff(q_type,type,
q: $i ).
tff(p_type,type,
p: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(not_type,type,
not: $i > $i ).
tff(axiom_type,type,
axiom: $i > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
<=> ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
<=> ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
<=> ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
tff(5,plain,
! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
| ( ifeq(theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))),true,theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))),true,theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))),true),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(X,Y) = or(not(X),Y) )
<=> ( implies(X,Y) = or(not(X),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
tff(14,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(or(p,q),r),or(p,or(q,r))) = or(not(or(or(p,q),r)),or(p,or(q,r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
implies(or(or(p,q),r),or(p,or(q,r))) = or(not(or(or(p,q),r)),or(p,or(q,r))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
or(not(or(or(p,q),r)),or(p,or(q,r))) = implies(or(or(p,q),r),or(p,or(q,r))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))) = theorem(implies(or(or(p,q),r),or(p,or(q,r)))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
theorem(implies(or(or(p,q),r),or(p,or(q,r)))) = theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(or(p,q),r),or(r,or(p,q))) = or(not(or(or(p,q),r)),or(r,or(p,q))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
implies(or(or(p,q),r),or(r,or(p,q))) = or(not(or(or(p,q),r)),or(r,or(p,q))),
inference(unit_resolution,[status(thm)],[22,16]) ).
tff(24,plain,
or(not(or(or(p,q),r)),or(r,or(p,q))) = implies(or(or(p,q),r),or(r,or(p,q))),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))) = theorem(implies(or(or(p,q),r),or(r,or(p,q)))),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
theorem(implies(or(or(p,q),r),or(r,or(p,q)))) = theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true) = theorem(implies(or(or(p,q),r),or(r,or(p,q)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
ifeq(true,true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true) = theorem(implies(or(or(p,q),r),or(r,or(p,q)))),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
^ [B: $i,A: $i] :
refl(( ( axiom(implies(or(A,B),or(B,A))) = true )
<=> ( axiom(implies(or(A,B),or(B,A))) = true ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true )
<=> ! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true )
<=> ! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
tff(40,plain,
! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true )
| ( axiom(implies(or(or(p,q),r),or(r,or(p,q)))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
axiom(implies(or(or(p,q),r),or(r,or(p,q)))) = true,
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
true = axiom(implies(or(or(p,q),r),or(r,or(p,q)))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
ifeq(true,true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true) = ifeq(axiom(implies(or(or(p,q),r),or(r,or(p,q)))),true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
ifeq(axiom(implies(or(or(p,q),r),or(r,or(p,q)))),true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true) = ifeq(true,true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [X: $i] :
refl(( ( ifeq(axiom(X),true,theorem(X),true) = true )
<=> ( ifeq(axiom(X),true,theorem(X),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
<=> ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
<=> ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
tff(52,plain,
! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(implies(or(or(p,q),r),or(r,or(p,q)))),true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
ifeq(axiom(implies(or(or(p,q),r),or(r,or(p,q)))),true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true) = true,
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
true = ifeq(axiom(implies(or(or(p,q),r),or(r,or(p,q)))),true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
true = theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))),
inference(transitivity,[status(thm)],[57,47,35,26]) ).
tff(59,plain,
ifeq(true,true,theorem(implies(or(or(p,q),r),or(p,or(q,r)))),true) = ifeq(theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))),true,theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))),true),
inference(monotonicity,[status(thm)],[58,21]) ).
tff(60,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(or(p,q),r),or(p,or(q,r)))),true) = theorem(implies(or(or(p,q),r),or(p,or(q,r)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
ifeq(true,true,theorem(implies(or(or(p,q),r),or(p,or(q,r)))),true) = theorem(implies(or(or(p,q),r),or(p,or(q,r)))),
inference(unit_resolution,[status(thm)],[60,33]) ).
tff(62,plain,
theorem(implies(or(or(p,q),r),or(p,or(q,r)))) = ifeq(true,true,theorem(implies(or(or(p,q),r),or(p,or(q,r)))),true),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))) = ifeq(theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))),true,theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))),true),
inference(transitivity,[status(thm)],[20,62,59]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true) = theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true) = theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),
inference(unit_resolution,[status(thm)],[64,33]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))) = or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))) = or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r)))),
inference(unit_resolution,[status(thm)],[66,16]) ).
tff(68,plain,
or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r)))) = implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r))))) = theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))) = theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r))))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))) = or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))) = or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r))),
inference(unit_resolution,[status(thm)],[71,16]) ).
tff(73,plain,
or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r))) = implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r)))) = theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))) = theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r)))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true) = theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true) = theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),
inference(unit_resolution,[status(thm)],[76,33]) ).
tff(78,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(r,or(p,q)),or(or(p,q),r)) = or(not(or(r,or(p,q))),or(or(p,q),r)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
implies(or(r,or(p,q)),or(or(p,q),r)) = or(not(or(r,or(p,q))),or(or(p,q),r)),
inference(unit_resolution,[status(thm)],[78,16]) ).
tff(80,plain,
or(not(or(r,or(p,q))),or(or(p,q),r)) = implies(or(r,or(p,q)),or(or(p,q),r)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
theorem(or(not(or(r,or(p,q))),or(or(p,q),r))) = theorem(implies(or(r,or(p,q)),or(or(p,q),r))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
theorem(implies(or(r,or(p,q)),or(or(p,q),r))) = theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true) = theorem(implies(or(r,or(p,q)),or(or(p,q),r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
ifeq(true,true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true) = theorem(implies(or(r,or(p,q)),or(or(p,q),r))),
inference(unit_resolution,[status(thm)],[83,33]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true )
| ( axiom(implies(or(r,or(p,q)),or(or(p,q),r))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
axiom(implies(or(r,or(p,q)),or(or(p,q),r))) = true,
inference(unit_resolution,[status(thm)],[85,42]) ).
tff(87,plain,
true = axiom(implies(or(r,or(p,q)),or(or(p,q),r))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
ifeq(true,true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true) = ifeq(axiom(implies(or(r,or(p,q)),or(or(p,q),r))),true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
ifeq(axiom(implies(or(r,or(p,q)),or(or(p,q),r))),true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true) = ifeq(true,true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(implies(or(r,or(p,q)),or(or(p,q),r))),true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
ifeq(axiom(implies(or(r,or(p,q)),or(or(p,q),r))),true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true) = true,
inference(unit_resolution,[status(thm)],[90,54]) ).
tff(92,plain,
true = ifeq(axiom(implies(or(r,or(p,q)),or(or(p,q),r))),true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
true = theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),
inference(transitivity,[status(thm)],[92,89,84,82]) ).
tff(94,plain,
ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true) = ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true) = ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))) = ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),
inference(symmetry,[status(thm)],[77]) ).
tff(97,plain,
theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))) = ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true) = theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true) = theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),
inference(unit_resolution,[status(thm)],[98,33]) ).
tff(100,plain,
implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))) = implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),
inference(monotonicity,[status(thm)],[79]) ).
tff(101,plain,
theorem(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))) = theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))) = theorem(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true )
<=> ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true )
<=> ! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true )
<=> ! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
tff(107,plain,
! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true )
| ( axiom(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
axiom(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))) = true,
inference(unit_resolution,[status(thm)],[110,109]) ).
tff(112,plain,
true = axiom(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true) = ifeq(axiom(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,theorem(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true),
inference(monotonicity,[status(thm)],[112,102]) ).
tff(114,plain,
ifeq(axiom(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,theorem(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true) = ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,theorem(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
ifeq(axiom(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,theorem(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true) = true,
inference(unit_resolution,[status(thm)],[115,54]) ).
tff(117,plain,
true = ifeq(axiom(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,theorem(implies(implies(or(r,or(p,q)),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
theorem(implies(or(r,or(p,q)),or(or(p,q),r))) = ifeq(true,true,theorem(implies(or(r,or(p,q)),or(or(p,q),r))),true),
inference(symmetry,[status(thm)],[84]) ).
tff(119,plain,
theorem(or(not(or(r,or(p,q))),or(or(p,q),r))) = theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),
inference(transitivity,[status(thm)],[81,118,88,91,117,114,99]) ).
tff(120,plain,
ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true) = ifeq(theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),true),
inference(monotonicity,[status(thm)],[119,97]) ).
tff(121,plain,
ifeq(theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),true) = ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
| ( ifeq(theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
ifeq(theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),true) = true,
inference(unit_resolution,[status(thm)],[122,7]) ).
tff(124,plain,
true = ifeq(theorem(implies(or(not(or(r,or(p,q))),or(or(p,q),r)),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true),true),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
true = theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r)))),
inference(transitivity,[status(thm)],[124,121,95,77,75]) ).
tff(126,plain,
ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true) = ifeq(theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true,theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),
inference(monotonicity,[status(thm)],[125,70]) ).
tff(127,plain,
ifeq(theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true,theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true) = ifeq(true,true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true) = theorem(implies(or(r,or(p,q)),or(p,or(q,r)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true) = theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),
inference(unit_resolution,[status(thm)],[128,33]) ).
tff(130,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(r,or(p,q)),or(p,or(q,r))) = or(not(or(r,or(p,q))),or(p,or(q,r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
implies(or(r,or(p,q)),or(p,or(q,r))) = or(not(or(r,or(p,q))),or(p,or(q,r))),
inference(unit_resolution,[status(thm)],[130,16]) ).
tff(132,plain,
or(not(or(r,or(p,q))),or(p,or(q,r))) = implies(or(r,or(p,q)),or(p,or(q,r))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))) = theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
theorem(implies(or(r,or(p,q)),or(p,or(q,r)))) = theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true) = ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),
inference(monotonicity,[status(thm)],[93,134]) ).
tff(136,plain,
ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true) = ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(implies(or(r,or(p,q)),or(p,or(r,q)))),true,theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
ifeq(axiom(implies(or(r,or(p,q)),or(p,or(r,q)))),true,theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),true) = true,
inference(unit_resolution,[status(thm)],[137,54]) ).
tff(139,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true )
<=> ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true )
<=> ! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
( ! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true )
<=> ! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,axiom,
! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
tff(143,plain,
! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ),
inference(skolemize,[status(sab)],[143]) ).
tff(145,plain,
! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true ),
inference(modus_ponens,[status(thm)],[144,140]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) = true )
| ( axiom(implies(or(r,or(p,q)),or(p,or(r,q)))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
axiom(implies(or(r,or(p,q)),or(p,or(r,q)))) = true,
inference(unit_resolution,[status(thm)],[146,145]) ).
tff(148,plain,
true = axiom(implies(or(r,or(p,q)),or(p,or(r,q)))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),true) = ifeq(axiom(implies(or(r,or(p,q)),or(p,or(r,q)))),true,theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),true),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),true) = theorem(implies(or(r,or(p,q)),or(p,or(r,q)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),true) = theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),
inference(unit_resolution,[status(thm)],[150,33]) ).
tff(152,plain,
theorem(implies(or(r,or(p,q)),or(p,or(r,q)))) = ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),true),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(r,or(p,q)),or(p,or(r,q))) = or(not(or(r,or(p,q))),or(p,or(r,q))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
implies(or(r,or(p,q)),or(p,or(r,q))) = or(not(or(r,or(p,q))),or(p,or(r,q))),
inference(unit_resolution,[status(thm)],[153,16]) ).
tff(155,plain,
or(not(or(r,or(p,q))),or(p,or(r,q))) = implies(or(r,or(p,q)),or(p,or(r,q))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))) = theorem(implies(or(r,or(p,q)),or(p,or(r,q)))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))) = theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),
inference(transitivity,[status(thm)],[156,152,149,138,92,89,84,82]) ).
tff(158,plain,
ifeq(theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true) = ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true) = ifeq(theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
theorem(implies(or(r,or(p,q)),or(p,or(q,r)))) = ifeq(true,true,theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true),
inference(symmetry,[status(thm)],[129]) ).
tff(161,plain,
theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))) = ifeq(theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),
inference(transitivity,[status(thm)],[133,160,135,159]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true) = theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true) = theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),
inference(unit_resolution,[status(thm)],[162,33]) ).
tff(164,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(p,or(r,q)),or(p,or(q,r))) = or(not(or(p,or(r,q))),or(p,or(q,r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
implies(or(p,or(r,q)),or(p,or(q,r))) = or(not(or(p,or(r,q))),or(p,or(q,r))),
inference(unit_resolution,[status(thm)],[164,16]) ).
tff(166,plain,
or(not(or(p,or(r,q))),or(p,or(q,r))) = implies(or(p,or(r,q)),or(p,or(q,r))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))) = theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
theorem(implies(or(p,or(r,q)),or(p,or(q,r)))) = theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true) = theorem(implies(or(p,or(r,q)),or(p,or(q,r)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
ifeq(true,true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true) = theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),
inference(unit_resolution,[status(thm)],[169,33]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = or(not(X),Y) )
| ( implies(or(r,q),or(q,r)) = or(not(or(r,q)),or(q,r)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
implies(or(r,q),or(q,r)) = or(not(or(r,q)),or(q,r)),
inference(unit_resolution,[status(thm)],[171,16]) ).
tff(173,plain,
or(not(or(r,q)),or(q,r)) = implies(or(r,q),or(q,r)),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
theorem(or(not(or(r,q)),or(q,r))) = theorem(implies(or(r,q),or(q,r))),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
theorem(implies(or(r,q),or(q,r))) = theorem(or(not(or(r,q)),or(q,r))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(r,q),or(q,r))),true) = theorem(implies(or(r,q),or(q,r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
ifeq(true,true,theorem(implies(or(r,q),or(q,r))),true) = theorem(implies(or(r,q),or(q,r))),
inference(unit_resolution,[status(thm)],[176,33]) ).
tff(178,plain,
( ~ ! [B: $i,A: $i] : ( axiom(implies(or(A,B),or(B,A))) = true )
| ( axiom(implies(or(r,q),or(q,r))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
axiom(implies(or(r,q),or(q,r))) = true,
inference(unit_resolution,[status(thm)],[178,42]) ).
tff(180,plain,
true = axiom(implies(or(r,q),or(q,r))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
ifeq(true,true,theorem(implies(or(r,q),or(q,r))),true) = ifeq(axiom(implies(or(r,q),or(q,r))),true,theorem(implies(or(r,q),or(q,r))),true),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
ifeq(axiom(implies(or(r,q),or(q,r))),true,theorem(implies(or(r,q),or(q,r))),true) = ifeq(true,true,theorem(implies(or(r,q),or(q,r))),true),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(implies(or(r,q),or(q,r))),true,theorem(implies(or(r,q),or(q,r))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
ifeq(axiom(implies(or(r,q),or(q,r))),true,theorem(implies(or(r,q),or(q,r))),true) = true,
inference(unit_resolution,[status(thm)],[183,54]) ).
tff(185,plain,
true = ifeq(axiom(implies(or(r,q),or(q,r))),true,theorem(implies(or(r,q),or(q,r))),true),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
true = theorem(or(not(or(r,q)),or(q,r))),
inference(transitivity,[status(thm)],[185,182,177,175]) ).
tff(187,plain,
ifeq(true,true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true) = ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true) = ifeq(true,true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
theorem(implies(or(p,or(r,q)),or(p,or(q,r)))) = ifeq(true,true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),
inference(symmetry,[status(thm)],[170]) ).
tff(190,plain,
theorem(implies(or(p,or(r,q)),or(p,or(q,r)))) = ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),
inference(transitivity,[status(thm)],[189,187]) ).
tff(191,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true) = theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
ifeq(true,true,theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true) = theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),
inference(unit_resolution,[status(thm)],[191,33]) ).
tff(193,plain,
implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r)))) = implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r)))),
inference(monotonicity,[status(thm)],[172]) ).
tff(194,plain,
theorem(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))) = theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))) = theorem(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true )
| ( axiom(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
axiom(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))) = true,
inference(unit_resolution,[status(thm)],[196,109]) ).
tff(198,plain,
true = axiom(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
ifeq(true,true,theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true) = ifeq(axiom(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,theorem(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true),
inference(monotonicity,[status(thm)],[198,195]) ).
tff(200,plain,
ifeq(axiom(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,theorem(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true) = ifeq(true,true,theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,theorem(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
ifeq(axiom(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,theorem(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true) = true,
inference(unit_resolution,[status(thm)],[201,54]) ).
tff(203,plain,
true = ifeq(axiom(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,theorem(implies(implies(or(r,q),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
theorem(implies(or(r,q),or(q,r))) = ifeq(true,true,theorem(implies(or(r,q),or(q,r))),true),
inference(symmetry,[status(thm)],[177]) ).
tff(205,plain,
theorem(or(not(or(r,q)),or(q,r))) = theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),
inference(transitivity,[status(thm)],[174,204,181,184,203,200,192]) ).
tff(206,plain,
ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true) = ifeq(theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),true),
inference(monotonicity,[status(thm)],[205,190]) ).
tff(207,plain,
ifeq(theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),true) = ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
| ( ifeq(theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
ifeq(theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),true) = true,
inference(unit_resolution,[status(thm)],[208,7]) ).
tff(210,plain,
true = ifeq(theorem(implies(or(not(or(r,q)),or(q,r)),implies(or(p,or(r,q)),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,q)),or(q,r))),true,theorem(implies(or(p,or(r,q)),or(p,or(q,r)))),true),true),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
true = theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),
inference(transitivity,[status(thm)],[210,207,188,170,168]) ).
tff(212,plain,
ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true) = ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true) = ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))) = ifeq(true,true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),
inference(symmetry,[status(thm)],[163]) ).
tff(215,plain,
theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))) = ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true) = theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
ifeq(true,true,theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true) = theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),
inference(unit_resolution,[status(thm)],[216,33]) ).
tff(218,plain,
implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))) = implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),
inference(monotonicity,[status(thm)],[165]) ).
tff(219,plain,
theorem(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))) = theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))) = theorem(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true )
| ( axiom(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
axiom(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))) = true,
inference(unit_resolution,[status(thm)],[221,109]) ).
tff(223,plain,
true = axiom(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
ifeq(true,true,theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true) = ifeq(axiom(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,theorem(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true),
inference(monotonicity,[status(thm)],[223,220]) ).
tff(225,plain,
ifeq(axiom(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,theorem(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true) = ifeq(true,true,theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,theorem(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
ifeq(axiom(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,theorem(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true) = true,
inference(unit_resolution,[status(thm)],[226,54]) ).
tff(228,plain,
true = ifeq(axiom(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,theorem(implies(implies(or(p,or(r,q)),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))) = theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),
inference(transitivity,[status(thm)],[167,189,187,206,209,228,225,217]) ).
tff(230,plain,
ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true) = ifeq(theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),true),
inference(monotonicity,[status(thm)],[229,215]) ).
tff(231,plain,
ifeq(theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),true) = ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
| ( ifeq(theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
ifeq(theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),true) = true,
inference(unit_resolution,[status(thm)],[232,7]) ).
tff(234,plain,
true = ifeq(theorem(implies(or(not(or(p,or(r,q))),or(p,or(q,r))),implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r)))))),true,ifeq(theorem(or(not(or(p,or(r,q))),or(p,or(q,r)))),true,theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true),true),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
theorem(or(not(or(r,or(p,q))),or(or(p,q),r))) = theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),
inference(transitivity,[status(thm)],[81,118,88,91,234,231,213,163]) ).
tff(236,plain,
ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true) = ifeq(theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),true),
inference(monotonicity,[status(thm)],[235,161]) ).
tff(237,plain,
ifeq(theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),true) = ifeq(theorem(or(not(or(r,or(p,q))),or(or(p,q),r))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
| ( ifeq(theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
ifeq(theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),true) = true,
inference(unit_resolution,[status(thm)],[238,7]) ).
tff(240,plain,
true = ifeq(theorem(implies(or(not(or(r,or(p,q))),or(p,or(r,q))),or(not(or(r,or(p,q))),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(r,or(p,q))),or(p,or(r,q)))),true,theorem(or(not(or(r,or(p,q))),or(p,or(q,r)))),true),true),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r)))) = theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),
inference(transitivity,[status(thm)],[74,96,94,120,123,240,237,136,129]) ).
tff(242,plain,
ifeq(theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true,theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true) = ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),
inference(monotonicity,[status(thm)],[241,69]) ).
tff(243,plain,
ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true) = ifeq(theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(or(p,q),r)))),true,theorem(or(not(or(not(or(or(p,q),r)),or(r,or(p,q)))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true) = ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
ifeq(true,true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true) = ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),
inference(unit_resolution,[status(thm)],[244,33]) ).
tff(246,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true) = theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(247,plain,
ifeq(true,true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true) = theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),
inference(unit_resolution,[status(thm)],[246,33]) ).
tff(248,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) = true )
| ( axiom(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(249,plain,
axiom(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))) = true,
inference(unit_resolution,[status(thm)],[248,109]) ).
tff(250,plain,
true = axiom(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
ifeq(true,true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true) = ifeq(axiom(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
ifeq(axiom(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true) = ifeq(true,true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
ifeq(axiom(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true) = true,
inference(unit_resolution,[status(thm)],[253,54]) ).
tff(255,plain,
true = ifeq(axiom(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
true = theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),
inference(transitivity,[status(thm)],[255,252,247]) ).
tff(257,plain,
ifeq(true,true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true) = ifeq(theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
ifeq(theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true) = ifeq(true,true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(theorem(implies(Y,X)),true,ifeq(theorem(Y),true,theorem(X),true),true) = true )
| ( ifeq(theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
ifeq(theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true) = true,
inference(unit_resolution,[status(thm)],[259,7]) ).
tff(261,plain,
true = ifeq(theorem(implies(implies(or(r,or(p,q)),or(p,or(q,r))),implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r)))))),true,ifeq(theorem(implies(or(r,or(p,q)),or(p,or(q,r)))),true,theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true),true),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
theorem(implies(or(or(p,q),r),or(r,or(p,q)))) = ifeq(true,true,theorem(implies(or(or(p,q),r),or(r,or(p,q)))),true),
inference(symmetry,[status(thm)],[35]) ).
tff(263,plain,
theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))) = theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),
inference(transitivity,[status(thm)],[25,262,46,56,261,258,245,243,127,65]) ).
tff(264,plain,
ifeq(theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))),true,theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))),true) = ifeq(theorem(implies(or(not(or(or(p,q),r)),or(r,or(p,q))),or(not(or(or(p,q),r)),or(p,or(q,r))))),true,ifeq(theorem(or(not(or(or(p,q),r)),or(r,or(p,q)))),true,theorem(or(not(or(or(p,q),r)),or(p,or(q,r)))),true),true),
inference(monotonicity,[status(thm)],[263,63]) ).
tff(265,plain,
theorem(implies(or(or(p,q),r),or(p,or(q,r)))) = true,
inference(transitivity,[status(thm)],[62,59,264,9]) ).
tff(266,plain,
( ( theorem(implies(or(or(p,q),r),or(p,or(q,r)))) != true )
<=> ( theorem(implies(or(or(p,q),r),or(p,or(q,r)))) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(267,axiom,
theorem(implies(or(or(p,q),r),or(p,or(q,r)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(268,plain,
theorem(implies(or(or(p,q),r),or(p,or(q,r)))) != true,
inference(modus_ponens,[status(thm)],[267,266]) ).
tff(269,plain,
$false,
inference(unit_resolution,[status(thm)],[268,265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL192-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n018.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 4 14:59:34 UTC 2026
% 0.07/0.35 % CPUTime :
% 162.53/162.80 % SZS status Unsatisfiable
% 162.53/162.80 % SZS output start Proof
% See solution above
% 0.14/164.11 % E exiting
%------------------------------------------------------------------------------