%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LDA007-2 : TPTP v9.0.0. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:17:05 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 51 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 62 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 6 ~; 2 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 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; 8 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(tk_type,type,
tk: $i ).
tff(tt_ts_type,type,
tt_ts: $i ).
tff(tsk_type,type,
tsk: $i ).
tff(t_type,type,
t: $i ).
tff(critical_point_type,type,
critical_point: $i > $i ).
tff(s_type,type,
s: $i ).
tff(k_type,type,
k: $i ).
tff(ts_type,type,
ts: $i ).
tff(tt_type,type,
tt: $i ).
tff(1,plain,
( ( k = critical_point(t) )
<=> ( k = critical_point(t) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
k = critical_point(t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
tff(3,plain,
k = critical_point(t),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
critical_point(t) = k,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
f(t,critical_point(t)) = f(t,k),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
f(t,k) = f(t,critical_point(t)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( tk = f(t,k) )
<=> ( tk = f(t,k) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
tk = f(t,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
tff(9,plain,
tk = f(t,k),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
tk = f(t,critical_point(t)),
inference(transitivity,[status(thm)],[9,6]) ).
tff(11,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(t,f(t,s)) = f(f(t,t),f(t,s)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
f(t,f(t,s)) = f(f(t,t),f(t,s)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
f(f(t,t),f(t,s)) = f(t,f(t,s)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ( ts = f(t,s) )
<=> ( ts = f(t,s) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
ts = f(t,s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(23,plain,
ts = f(t,s),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
f(t,s) = ts,
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ( tt = f(t,t) )
<=> ( tt = f(t,t) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
tt = f(t,t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
tff(27,plain,
tt = f(t,t),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
f(t,t) = tt,
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
f(f(t,t),f(t,s)) = f(tt,ts),
inference(monotonicity,[status(thm)],[28,24]) ).
tff(30,plain,
f(tt,ts) = f(f(t,t),f(t,s)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ( tt_ts = f(tt,ts) )
<=> ( tt_ts = f(tt,ts) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
tt_ts = f(tt,ts),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
tff(33,plain,
tt_ts = f(tt,ts),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
tt_ts = f(t,f(t,s)),
inference(transitivity,[status(thm)],[33,30,20]) ).
tff(35,plain,
f(tt_ts,tk) = f(f(t,f(t,s)),f(t,critical_point(t))),
inference(monotonicity,[status(thm)],[34,10]) ).
tff(36,plain,
f(f(t,f(t,s)),f(t,critical_point(t))) = f(tt_ts,tk),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(t,f(f(t,s),critical_point(t))) = f(f(t,f(t,s)),f(t,critical_point(t))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
f(t,f(f(t,s),critical_point(t))) = f(f(t,f(t,s)),f(t,critical_point(t))),
inference(unit_resolution,[status(thm)],[37,17]) ).
tff(39,plain,
( ( tsk = f(ts,k) )
<=> ( tsk = f(ts,k) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
tsk = f(ts,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
tff(41,plain,
tsk = f(ts,k),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
f(ts,k) = tsk,
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
f(f(t,s),critical_point(t)) = f(ts,k),
inference(monotonicity,[status(thm)],[24,4]) ).
tff(44,plain,
f(f(t,s),critical_point(t)) = tsk,
inference(transitivity,[status(thm)],[43,42]) ).
tff(45,plain,
f(t,f(f(t,s),critical_point(t))) = f(t,tsk),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
f(t,tsk) = f(t,f(f(t,s),critical_point(t))),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
f(t,tsk) = f(tt_ts,tk),
inference(transitivity,[status(thm)],[46,38,36]) ).
tff(48,plain,
( ( f(t,tsk) != f(tt_ts,tk) )
<=> ( f(t,tsk) != f(tt_ts,tk) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
f(t,tsk) != f(tt_ts,tk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
tff(50,plain,
f(t,tsk) != f(tt_ts,tk),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LDA007-2 : TPTP v9.0.0. Bugfixed v2.6.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 23:21:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------