%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n014.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 02:59:29 PM UTC 2026
% Result : Unsatisfiable 1.97s 2.21s
% Output : Proof 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 62 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 83 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 10 ~; 6 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 5 ( 5 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 : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 113 ( 102 !; 0 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(theorem_type,type,
theorem: $i > $i ).
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(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(axiom_type,type,
axiom: $i > $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true )
<=> ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true )
<=> ! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true )
<=> ! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true )
| ( ifeq(theorem(or(not(or(q,not(p))),or(not(p),q))),true,ifeq(axiom(or(not(not(p)),or(q,not(p)))),true,theorem(or(not(not(p)),or(not(p),q))),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(theorem(or(not(or(q,not(p))),or(not(p),q))),true,ifeq(axiom(or(not(not(p)),or(q,not(p)))),true,theorem(or(not(not(p)),or(not(p),q))),true),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i] :
refl(( ( axiom(or(not(A),or(B,A))) = true )
<=> ( axiom(or(not(A),or(B,A))) = true ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true )
<=> ! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true )
<=> ! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
tff(14,plain,
! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i] : ( axiom(or(not(A),or(B,A))) = true )
| ( axiom(or(not(not(p)),or(q,not(p)))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
axiom(or(not(not(p)),or(q,not(p)))) = true,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
true = axiom(or(not(not(p)),or(q,not(p)))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
ifeq(true,true,theorem(or(not(not(p)),or(not(p),q))),true) = ifeq(axiom(or(not(not(p)),or(q,not(p)))),true,theorem(or(not(not(p)),or(not(p),q))),true),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(or(not(not(p)),or(not(p),q))),true) = theorem(or(not(not(p)),or(not(p),q))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
ifeq(true,true,theorem(or(not(not(p)),or(not(p),q))),true) = theorem(or(not(not(p)),or(not(p),q))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
theorem(or(not(not(p)),or(not(p),q))) = ifeq(true,true,theorem(or(not(not(p)),or(not(p),q))),true),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
theorem(or(not(not(p)),or(not(p),q))) = ifeq(axiom(or(not(not(p)),or(q,not(p)))),true,theorem(or(not(not(p)),or(not(p),q))),true),
inference(transitivity,[status(thm)],[30,20]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,theorem(or(not(or(q,not(p))),or(not(p),q))),true) = theorem(or(not(or(q,not(p))),or(not(p),q))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
ifeq(true,true,theorem(or(not(or(q,not(p))),or(not(p),q))),true) = theorem(or(not(or(q,not(p))),or(not(p),q))),
inference(unit_resolution,[status(thm)],[32,27]) ).
tff(34,plain,
^ [B: $i,A: $i] :
refl(( ( axiom(or(not(or(A,B)),or(B,A))) = true )
<=> ( axiom(or(not(or(A,B)),or(B,A))) = true ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true )
<=> ! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true )
<=> ! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
tff(38,plain,
! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i] : ( axiom(or(not(or(A,B)),or(B,A))) = true )
| ( axiom(or(not(or(q,not(p))),or(not(p),q))) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
axiom(or(not(or(q,not(p))),or(not(p),q))) = true,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
true = axiom(or(not(or(q,not(p))),or(not(p),q))),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
ifeq(true,true,theorem(or(not(or(q,not(p))),or(not(p),q))),true) = ifeq(axiom(or(not(or(q,not(p))),or(not(p),q))),true,theorem(or(not(or(q,not(p))),or(not(p),q))),true),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
ifeq(axiom(or(not(or(q,not(p))),or(not(p),q))),true,theorem(or(not(or(q,not(p))),or(not(p),q))),true) = ifeq(true,true,theorem(or(not(or(q,not(p))),or(not(p),q))),true),
inference(symmetry,[status(thm)],[44]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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(49,axiom,
! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
tff(50,plain,
! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [X: $i] : ( ifeq(axiom(X),true,theorem(X),true) = true )
| ( ifeq(axiom(or(not(or(q,not(p))),or(not(p),q))),true,theorem(or(not(or(q,not(p))),or(not(p),q))),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
ifeq(axiom(or(not(or(q,not(p))),or(not(p),q))),true,theorem(or(not(or(q,not(p))),or(not(p),q))),true) = true,
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
true = ifeq(axiom(or(not(or(q,not(p))),or(not(p),q))),true,theorem(or(not(or(q,not(p))),or(not(p),q))),true),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
axiom(or(not(not(p)),or(q,not(p)))) = theorem(or(not(or(q,not(p))),or(not(p),q))),
inference(transitivity,[status(thm)],[18,55,45,33]) ).
tff(57,plain,
ifeq(axiom(or(not(not(p)),or(q,not(p)))),true,theorem(or(not(not(p)),or(not(p),q))),true) = ifeq(theorem(or(not(or(q,not(p))),or(not(p),q))),true,ifeq(axiom(or(not(not(p)),or(q,not(p)))),true,theorem(or(not(not(p)),or(not(p),q))),true),true),
inference(monotonicity,[status(thm)],[56,31]) ).
tff(58,plain,
theorem(or(not(not(p)),or(not(p),q))) = true,
inference(transitivity,[status(thm)],[30,20,57,9]) ).
tff(59,plain,
( ( theorem(or(not(not(p)),or(not(p),q))) != true )
<=> ( theorem(or(not(not(p)),or(not(p),q))) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
theorem(or(not(not(p)),or(not(p),q))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(61,plain,
theorem(or(not(not(p)),or(not(p),q))) != true,
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 11:49:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 1.97/2.21 % SZS status Unsatisfiable
% 1.97/2.21 % SZS output start Proof
% See solution above
% 1.97/2.24 % E exiting
%------------------------------------------------------------------------------