%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL218-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.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 02:59:35 PM UTC 2026
% Result : Unsatisfiable 6.79s 7.12s
% Output : Proof 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 44
% Syntax : Number of formulae : 100 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 434 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 616 ( 290 ~; 285 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 251 ( 233 !; 0 ?; 251 :)
% Comments :
%------------------------------------------------------------------------------
tff(theorem_type,type,
theorem: $i > $o ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(q_type,type,
q: $i ).
tff(not_type,type,
not: $i > $i ).
tff(p_type,type,
p: $i ).
tff(axiom_type,type,
axiom: $i > $o ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
<=> axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
<=> ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
<=> ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL003-0.ax',axiom_1_5) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| axiom(or(not(or(not(p),or(not(or(not(or(p,q)),q)),q))),or(not(or(not(or(p,q)),q)),or(not(p),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
axiom(or(not(or(not(p),or(not(or(not(or(p,q)),q)),q))),or(not(or(not(or(p,q)),q)),or(not(p),q)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ theorem(or(not(or(not(or(p,q)),q)),or(not(p),q)))
<=> ~ theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(12,plain,
~ theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [Y: $i,X: $i] :
refl(( ( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
<=> ( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
<=> ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
<=> ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [Y: $i,X: $i] :
rewrite(( ( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) )
<=> ( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [Y: $i,X: $i] :
( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) )
<=> ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [Y: $i,X: $i] :
( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL003-0.ax',rule_2) ).
tff(19,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(not(or(p,q)),q)),or(not(p),q)))
| ~ theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(or(not(p),or(not(or(not(or(p,q)),q)),q))),or(not(or(not(or(p,q)),q)),or(not(p),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(not(or(p,q)),q)),or(not(p),q)))
| ~ theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(or(not(p),or(not(or(not(or(p,q)),q)),q))),or(not(or(not(or(p,q)),q)),or(not(p),q)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(not(or(p,q)),q)),or(not(p),q)))
| ~ theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(or(not(p),or(not(or(not(or(p,q)),q)),q))),or(not(or(not(or(p,q)),q)),or(not(p),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(not(or(p,q)),q)),or(not(p),q)))
| ~ theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(or(not(p),or(not(or(not(or(p,q)),q)),q))),or(not(or(not(or(p,q)),q)),or(not(p),q)))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ theorem(or(not(p),or(not(or(not(or(p,q)),q)),q))),
inference(unit_resolution,[status(thm)],[25,22,12,9]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
^ [B: $i,A: $i] :
refl(( axiom(or(not(or(A,B)),or(B,A)))
<=> axiom(or(not(or(A,B)),or(B,A))) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
<=> ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
<=> ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL003-0.ax',axiom_1_4) ).
tff(33,plain,
! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
| axiom(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
axiom(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
^ [X: $i] :
refl(( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL003-0.ax',rule_1) ).
tff(42,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))),
inference(unit_resolution,[status(thm)],[47,44,37]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
| axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q))))),
inference(unit_resolution,[status(thm)],[49,35]) ).
tff(51,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
<=> ( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( theorem(or(not(X),Z))
| ~ axiom(or(not(X),Y))
| ~ theorem(or(not(Y),Z)) )
<=> ( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [Z: $i,Y: $i,X: $i] :
( theorem(or(not(X),Z))
| ~ axiom(or(not(X),Y))
| ~ theorem(or(not(Y),Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [Z: $i,Y: $i,X: $i] :
( theorem(or(not(X),Z))
| ~ axiom(or(not(X),Y))
| ~ theorem(or(not(Y),Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL003-0.ax',rule_3) ).
tff(57,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))) )
<=> ( ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(not(or(p,q)),q)),or(q,not(or(p,q)))))
| theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ theorem(or(not(or(q,not(or(p,q)))),or(not(or(p,q)),q))) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),
inference(unit_resolution,[status(thm)],[66,60,50,48]) ).
tff(68,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))))
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))))
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))) )
<=> ( ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))))
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))))
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))))
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| ~ theorem(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q)))
| ~ axiom(or(not(or(not(or(not(or(p,q)),q)),or(not(or(p,q)),q))),or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))))
| theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q))),
inference(unit_resolution,[status(thm)],[73,22,67,28]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
| axiom(or(not(or(q,p)),or(p,q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
axiom(or(not(or(q,p)),or(p,q))),
inference(unit_resolution,[status(thm)],[75,35]) ).
tff(77,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(q,p)),or(p,q)))
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(q,p)),or(p,q)))
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ( ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(or(q,p)),or(p,q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ axiom(or(not(or(q,p)),or(p,q)))
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(or(q,p)),or(p,q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(q,p)),or(p,q)))
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(or(q,p)),or(p,q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(q,p)),or(p,q)))
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(or(q,p)),or(p,q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(or(q,p)),or(p,q)))
| ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ theorem(or(not(or(p,q)),or(not(or(not(or(p,q)),q)),q)))
| theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ),
inference(unit_resolution,[status(thm)],[82,60,76]) ).
tff(84,plain,
theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))),
inference(unit_resolution,[status(thm)],[83,74]) ).
tff(85,plain,
^ [B: $i,A: $i] :
refl(( axiom(or(not(A),or(B,A)))
<=> axiom(or(not(A),or(B,A))) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [B: $i,A: $i] : axiom(or(not(A),or(B,A)))
<=> ! [B: $i,A: $i] : axiom(or(not(A),or(B,A))) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [B: $i,A: $i] : axiom(or(not(A),or(B,A)))
<=> ! [B: $i,A: $i] : axiom(or(not(A),or(B,A))) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
! [B: $i,A: $i] : axiom(or(not(A),or(B,A))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL003-0.ax',axiom_1_3) ).
tff(89,plain,
! [B: $i,A: $i] : axiom(or(not(A),or(B,A))),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [B: $i,A: $i] : axiom(or(not(A),or(B,A))),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [B: $i,A: $i] : axiom(or(not(A),or(B,A))),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ~ ! [B: $i,A: $i] : axiom(or(not(A),or(B,A)))
| axiom(or(not(p),or(q,p))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
axiom(or(not(p),or(q,p))),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q)))
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) )
| ~ axiom(or(not(p),or(q,p)))
| theorem(or(not(p),or(not(or(not(or(p,q)),q)),q)))
| ~ theorem(or(not(or(q,p)),or(not(or(not(or(p,q)),q)),q))) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
$false,
inference(unit_resolution,[status(thm)],[99,60,93,84,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL218-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 15:10:07 UTC 2026
% 0.07/0.35 % CPUTime :
% 6.79/7.12 % SZS status Unsatisfiable
% 6.79/7.12 % SZS output start Proof
% See solution above
% 0.15/7.21 % E exiting
%------------------------------------------------------------------------------