%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TIM031_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Tue May 5 07:17:47 PM UTC 2026
% Result : Theorem 0.18s 0.35s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 37
% Syntax : Number of formulae : 72 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 392 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 571 ( 265 ~; 249 |; 16 &)
% ( 38 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 168 ( 162 !; 0 ?; 168 :)
% Comments :
%------------------------------------------------------------------------------
tff(before_type,type,
before: ( interval * interval ) > $o ).
tff(h_type,type,
h: interval ).
tff(d_type,type,
d: interval ).
tff(f_type,type,
f: interval ).
tff(g_type,type,
g: interval ).
tff(e_type,type,
e: interval ).
tff(a_type,type,
a: interval ).
tff(c_type,type,
c: interval ).
tff(b_type,type,
b: interval ).
tff(1,plain,
( before(g,h)
<=> before(g,h) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
before(g,h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
tff(3,plain,
before(g,h),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( before(f,g)
<=> before(f,g) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
before(f,g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
tff(6,plain,
before(f,g),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
<=> ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
^ [I: interval,J: interval,K: interval] :
trans(monotonicity(trans(monotonicity(rewrite(( ( before(I,J)
& before(J,K) )
<=> ~ ( ~ before(I,J)
| ~ before(J,K) ) )),
( ~ ( before(I,J)
& before(J,K) )
<=> ~ ~ ( ~ before(I,J)
| ~ before(J,K) ) )),
rewrite(( ~ ~ ( ~ before(I,J)
| ~ before(J,K) )
<=> ( ~ before(I,J)
| ~ before(J,K) ) )),
( ~ ( before(I,J)
& before(J,K) )
<=> ( ~ before(I,J)
| ~ before(J,K) ) )),
( ( ~ ( before(I,J)
& before(J,K) )
| before(I,K) )
<=> ( ~ before(I,J)
| ~ before(J,K)
| before(I,K) ) )),
rewrite(( ( ~ before(I,J)
| ~ before(J,K)
| before(I,K) )
<=> ( before(I,K)
| ~ before(I,J)
| ~ before(J,K) ) )),
( ( ~ ( before(I,J)
& before(J,K) )
| before(I,K) )
<=> ( before(I,K)
| ~ before(I,J)
| ~ before(J,K) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [I: interval,J: interval,K: interval] :
( ~ ( before(I,J)
& before(J,K) )
| before(I,K) )
<=> ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [I: interval,J: interval,K: interval] :
( ~ ( before(I,J)
& before(J,K) )
| before(I,K) )
<=> ! [I: interval,J: interval,K: interval] :
( ~ ( before(I,J)
& before(J,K) )
| before(I,K) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [I: interval,J: interval,K: interval] :
rewrite(( ( ( before(I,J)
& before(J,K) )
=> before(I,K) )
<=> ( ~ ( before(I,J)
& before(J,K) )
| before(I,K) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [I: interval,J: interval,K: interval] :
( ( before(I,J)
& before(J,K) )
=> before(I,K) )
<=> ! [I: interval,J: interval,K: interval] :
( ~ ( before(I,J)
& before(J,K) )
| before(I,K) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [I: interval,J: interval,K: interval] :
( ( before(I,J)
& before(J,K) )
=> before(I,K) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TIM002_0.ax',before_transitive) ).
tff(14,plain,
! [I: interval,J: interval,K: interval] :
( ~ ( before(I,J)
& before(J,K) )
| before(I,K) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [I: interval,J: interval,K: interval] :
( ~ ( before(I,J)
& before(J,K) )
| before(I,K) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [I: interval,J: interval,K: interval] :
( ~ ( before(I,J)
& before(J,K) )
| before(I,K) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(f,g)
| before(f,h)
| ~ before(g,h) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(f,g)
| before(f,h)
| ~ before(g,h) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ( before(f,h)
| ~ before(f,g)
| ~ before(g,h) )
<=> ( ~ before(f,g)
| before(f,h)
| ~ before(g,h) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(f,h)
| ~ before(f,g)
| ~ before(g,h) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(f,g)
| before(f,h)
| ~ before(g,h) ) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(f,h)
| ~ before(f,g)
| ~ before(g,h) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(f,g)
| before(f,h)
| ~ before(g,h) ) ),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(f,h)
| ~ before(f,g)
| ~ before(g,h) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(f,g)
| before(f,h)
| ~ before(g,h) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
before(f,h),
inference(unit_resolution,[status(thm)],[24,18,6,3]) ).
tff(26,plain,
( before(e,f)
<=> before(e,f) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
before(e,f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
tff(28,plain,
before(e,f),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( before(d,e)
<=> before(d,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
before(d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
tff(31,plain,
before(d,e),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,e)
| before(d,f)
| ~ before(e,f) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,e)
| before(d,f)
| ~ before(e,f) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( before(d,f)
| ~ before(d,e)
| ~ before(e,f) )
<=> ( ~ before(d,e)
| before(d,f)
| ~ before(e,f) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(d,f)
| ~ before(d,e)
| ~ before(e,f) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,e)
| before(d,f)
| ~ before(e,f) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(d,f)
| ~ before(d,e)
| ~ before(e,f) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,e)
| before(d,f)
| ~ before(e,f) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(d,f)
| ~ before(d,e)
| ~ before(e,f) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,e)
| before(d,f)
| ~ before(e,f) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
before(d,f),
inference(unit_resolution,[status(thm)],[37,18,31,28]) ).
tff(39,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,f)
| before(d,h)
| ~ before(f,h) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,f)
| before(d,h)
| ~ before(f,h) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( before(d,h)
| ~ before(d,f)
| ~ before(f,h) )
<=> ( ~ before(d,f)
| before(d,h)
| ~ before(f,h) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(d,h)
| ~ before(d,f)
| ~ before(f,h) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,f)
| before(d,h)
| ~ before(f,h) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(d,h)
| ~ before(d,f)
| ~ before(f,h) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,f)
| before(d,h)
| ~ before(f,h) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(d,h)
| ~ before(d,f)
| ~ before(f,h) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(d,f)
| before(d,h)
| ~ before(f,h) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
before(d,h),
inference(unit_resolution,[status(thm)],[44,18,38,25]) ).
tff(46,plain,
( before(b,c)
<=> before(b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
before(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
tff(48,plain,
before(b,c),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( before(a,b)
<=> before(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
before(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(51,plain,
before(a,b),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,c)
| ~ before(a,b)
| ~ before(b,c) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,c)
| ~ before(a,b)
| ~ before(b,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,c)
| ~ before(a,b)
| ~ before(b,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,c)
| ~ before(a,b)
| ~ before(b,c) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
before(a,c),
inference(unit_resolution,[status(thm)],[54,18,51,48]) ).
tff(56,plain,
( before(c,d)
<=> before(c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
before(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
tff(58,plain,
before(c,d),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(c,d)
| before(a,d)
| ~ before(a,c) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(c,d)
| before(a,d)
| ~ before(a,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( before(a,d)
| ~ before(a,c)
| ~ before(c,d) )
<=> ( ~ before(c,d)
| before(a,d)
| ~ before(a,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,d)
| ~ before(a,c)
| ~ before(c,d) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(c,d)
| before(a,d)
| ~ before(a,c) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,d)
| ~ before(a,c)
| ~ before(c,d) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(c,d)
| before(a,d)
| ~ before(a,c) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,d)
| ~ before(a,c)
| ~ before(c,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| ~ before(c,d)
| before(a,d)
| ~ before(a,c) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
before(a,d),
inference(unit_resolution,[status(thm)],[64,18,58,55]) ).
tff(66,plain,
( ~ before(a,h)
<=> ~ before(a,h) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
~ before(a,h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(68,plain,
~ before(a,h),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,h)
| ~ before(a,d)
| ~ before(d,h) )
<=> ( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,h)
| ~ before(a,d)
| ~ before(d,h) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,h)
| ~ before(a,d)
| ~ before(d,h) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [I: interval,J: interval,K: interval] :
( before(I,K)
| ~ before(I,J)
| ~ before(J,K) )
| before(a,h)
| ~ before(a,d)
| ~ before(d,h) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
$false,
inference(unit_resolution,[status(thm)],[71,18,68,65,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : TIM031_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.31 % Computer : n011.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon May 4 18:30:04 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.18/0.35 % SZS status Theorem
% 0.18/0.35 % SZS output start Proof
% See solution above
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------