%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM027-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:18:42 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 93 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 426 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 536 ( 224 ~; 267 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 240 ( 219 !; 0 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(1,plain,
( less(multiply(b,c),multiply(a,c))
<=> less(multiply(b,c),multiply(a,c)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
less(multiply(b,c),multiply(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_c_less_than_a_times_c) ).
tff(3,plain,
less(multiply(b,c),multiply(a,c)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,A: $i] :
refl(( ( ~ equalish(A,B)
| ~ less(A,B) )
<=> ( ~ equalish(A,B)
| ~ less(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) )
<=> ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) )
<=> ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [B: $i,A: $i] :
rewrite(( ( ~ less(A,B)
| ~ equalish(A,B) )
<=> ( ~ equalish(A,B)
| ~ less(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,A: $i] :
( ~ less(A,B)
| ~ equalish(A,B) )
<=> ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [B: $i,A: $i] :
( ~ less(A,B)
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_and_equal) ).
tff(10,plain,
! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) )
| ~ equalish(multiply(b,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) )
| ~ equalish(multiply(b,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) )
| ~ equalish(multiply(b,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [B: $i,A: $i] :
( ~ equalish(A,B)
| ~ less(A,B) )
| ~ equalish(multiply(b,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ equalish(multiply(b,c),multiply(a,c)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) )
<=> ( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_preserved_over_times) ).
tff(22,plain,
! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) )
| ~ equalish(b,a)
| equalish(multiply(b,c),multiply(a,c)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) )
| ~ equalish(b,a)
| equalish(multiply(b,c),multiply(a,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) )
| ~ equalish(b,a)
| equalish(multiply(b,c),multiply(a,c)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) )
| ~ equalish(b,a)
| equalish(multiply(b,c),multiply(a,c)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ equalish(b,a)
| equalish(multiply(b,c),multiply(a,c)) ),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,plain,
~ equalish(b,a),
inference(unit_resolution,[status(thm)],[28,17]) ).
tff(30,plain,
( ~ less(b,a)
<=> ~ less(b,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
~ less(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_less_than_a) ).
tff(32,plain,
~ less(b,a),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
^ [B: $i,A: $i] :
refl(( ( equalish(B,A)
| less(A,B)
| less(B,A) )
<=> ( equalish(B,A)
| less(A,B)
| less(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) )
<=> ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) )
<=> ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [B: $i,A: $i] :
trans(monotonicity(rewrite(( ( less(A,B)
| equalish(B,A) )
<=> ( equalish(B,A)
| less(A,B) ) )),
( ( less(A,B)
| equalish(B,A)
| less(B,A) )
<=> ( equalish(B,A)
| less(A,B)
| less(B,A) ) )),
rewrite(( ( equalish(B,A)
| less(A,B)
| less(B,A) )
<=> ( equalish(B,A)
| less(A,B)
| less(B,A) ) )),
( ( less(A,B)
| equalish(B,A)
| less(B,A) )
<=> ( equalish(B,A)
| less(A,B)
| less(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [B: $i,A: $i] :
( less(A,B)
| equalish(B,A)
| less(B,A) )
<=> ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [B: $i,A: $i] :
( less(A,B)
| equalish(B,A)
| less(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_either_less_or_equal) ).
tff(39,plain,
! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) )
| equalish(b,a)
| less(a,b)
| less(b,a) )
<=> ( ~ ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) )
| equalish(b,a)
| less(a,b)
| less(b,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) )
| equalish(b,a)
| less(a,b)
| less(b,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i] :
( equalish(B,A)
| less(A,B)
| less(B,A) )
| equalish(b,a)
| less(a,b)
| less(b,a) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( equalish(b,a)
| less(a,b) ),
inference(unit_resolution,[status(thm)],[45,42,32]) ).
tff(47,plain,
less(a,b),
inference(unit_resolution,[status(thm)],[46,29]) ).
tff(48,plain,
( ~ equalish(c,n0)
<=> ~ equalish(c,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
~ equalish(c,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_is_0) ).
tff(50,plain,
~ equalish(c,n0),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
<=> ( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(( ( ~ less(A,B)
| equalish(C,n0)
| less(multiply(A,C),multiply(B,C)) )
<=> ( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| equalish(C,n0)
| less(multiply(A,C),multiply(B,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| equalish(C,n0)
| less(multiply(A,C),multiply(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_lemma) ).
tff(57,plain,
! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
| equalish(c,n0)
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
| equalish(c,n0)
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ less(a,b)
| less(multiply(a,c),multiply(b,c))
| equalish(c,n0) )
<=> ( equalish(c,n0)
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c))
| equalish(c,n0) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
| equalish(c,n0)
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c)) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c))
| equalish(c,n0) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
| equalish(c,n0)
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c)) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c))
| equalish(c,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| less(multiply(A,C),multiply(B,C))
| equalish(C,n0) )
| equalish(c,n0)
| ~ less(a,b)
| less(multiply(a,c),multiply(b,c)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ less(a,b)
| less(multiply(a,c),multiply(b,c)) ),
inference(unit_resolution,[status(thm)],[66,60,50]) ).
tff(68,plain,
less(multiply(a,c),multiply(b,c)),
inference(unit_resolution,[status(thm)],[67,47]) ).
tff(69,plain,
( ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( ~ less(A,B)
| ~ less(C,A) )
<=> ( ~ less(C,A)
| ~ less(A,B) ) )),
( ( ~ less(A,B)
| ~ less(C,A)
| less(C,B) )
<=> ( ~ less(C,A)
| ~ less(A,B)
| less(C,B) ) )),
rewrite(( ( ~ less(C,A)
| ~ less(A,B)
| less(C,B) )
<=> ( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) )),
( ( ~ less(A,B)
| ~ less(C,A)
| less(C,B) )
<=> ( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) )
<=> ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [B: $i,A: $i,C: $i] :
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
tff(74,plain,
! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(multiply(a,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(multiply(a,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( less(multiply(a,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c))
| ~ less(multiply(b,c),multiply(a,c)) )
<=> ( less(multiply(a,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(multiply(a,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c))
| ~ less(multiply(b,c),multiply(a,c)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(multiply(a,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c)) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(multiply(a,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c))
| ~ less(multiply(b,c),multiply(a,c)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(multiply(a,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c)) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(multiply(a,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c))
| ~ less(multiply(b,c),multiply(a,c)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) )
| less(multiply(a,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c))
| ~ less(multiply(a,c),multiply(b,c)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
less(multiply(a,c),multiply(a,c)),
inference(unit_resolution,[status(thm)],[83,77,3,68]) ).
tff(85,plain,
^ [A: $i] :
refl(( ~ less(A,A)
<=> ~ less(A,A) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [A: $i] : ~ less(A,A)
<=> ! [A: $i] : ~ less(A,A) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [A: $i] : ~ less(A,A)
<=> ! [A: $i] : ~ less(A,A) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
! [A: $i] : ~ less(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_not_less_than_itself) ).
tff(89,plain,
! [A: $i] : ~ less(A,A),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [A: $i] : ~ less(A,A),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [A: $i] : ~ less(A,A),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ~ ! [A: $i] : ~ less(A,A)
| ~ less(multiply(a,c),multiply(a,c)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
$false,
inference(unit_resolution,[status(thm)],[92,91,84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM027-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 23:59:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% See solution above
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------