TSTP Solution File: GRP669-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP669-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Fri Sep 16 22:29:23 EDT 2022
% Result : Unsatisfiable 0.19s 0.57s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 73
% Syntax : Number of formulae : 255 ( 191 unt; 7 typ; 0 def)
% Number of atoms : 321 ( 312 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 109 ( 44 ~; 40 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 252 ( 234 !; 0 ?; 252 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(unit_type,type,
unit: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
tff(5,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(b,c),mult(mult(b,c),mult(mult(mult(a,mult(b,c)),a),b))) = mult(mult(mult(a,mult(b,c)),a),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ld(mult(b,c),mult(mult(b,c),mult(mult(mult(a,mult(b,c)),a),b))) = mult(mult(mult(a,mult(b,c)),a),b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
<=> ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(b,c),mult(mult(mult(a,mult(b,c)),a),b)) = mult(b,mult(mult(c,mult(mult(a,mult(b,c)),a)),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
mult(mult(b,c),mult(mult(mult(a,mult(b,c)),a),b)) = mult(b,mult(mult(c,mult(mult(a,mult(b,c)),a)),b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
mult(b,mult(mult(c,mult(mult(a,mult(b,c)),a)),b)) = mult(mult(b,c),mult(mult(mult(a,mult(b,c)),a),b)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [A: $i] :
refl(
( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
tff(24,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(b,mult(c,a)),unit) = mult(b,mult(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
mult(mult(b,mult(c,a)),unit) = mult(b,mult(c,a)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
mult(b,mult(c,a)) = mult(mult(b,mult(c,a)),unit),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
^ [A: $i] :
refl(
( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
tff(34,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(c,a)) = mult(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
mult(unit,mult(c,a)) = mult(c,a),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
mult(c,a) = mult(unit,mult(c,a)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
mult(mult(c,a),mult(b,mult(c,a))) = mult(mult(unit,mult(c,a)),mult(mult(b,mult(c,a)),unit)),
inference(monotonicity,[status(thm)],[39,29]) ).
tff(41,plain,
mult(mult(unit,mult(c,a)),mult(mult(b,mult(c,a)),unit)) = mult(mult(c,a),mult(b,mult(c,a))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
<=> ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
tff(46,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(unit,mult(c,a)),mult(mult(b,mult(c,a)),unit)) = mult(mult(unit,mult(mult(c,a),mult(b,mult(c,a)))),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
mult(mult(unit,mult(c,a)),mult(mult(b,mult(c,a)),unit)) = mult(mult(unit,mult(mult(c,a),mult(b,mult(c,a)))),unit),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
mult(mult(unit,mult(mult(c,a),mult(b,mult(c,a)))),unit) = mult(mult(unit,mult(c,a)),mult(mult(b,mult(c,a)),unit)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
<=> ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
tff(56,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(unit,mult(mult(c,a),mult(b,mult(c,a)))) = mult(mult(mult(unit,mult(c,a)),b),mult(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
mult(unit,mult(mult(c,a),mult(b,mult(c,a)))) = mult(mult(mult(unit,mult(c,a)),b),mult(c,a)),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
mult(mult(mult(unit,mult(c,a)),b),mult(c,a)) = mult(unit,mult(mult(c,a),mult(b,mult(c,a)))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
mult(mult(unit,mult(c,a)),b) = mult(mult(c,a),b),
inference(monotonicity,[status(thm)],[38]) ).
tff(63,plain,
mult(mult(mult(unit,mult(c,a)),b),mult(c,a)) = mult(mult(mult(c,a),b),mult(c,a)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
mult(mult(mult(c,a),b),mult(c,a)) = mult(mult(mult(unit,mult(c,a)),b),mult(c,a)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
mult(mult(mult(c,a),b),mult(c,a)) = mult(unit,mult(mult(c,a),mult(b,mult(c,a)))),
inference(transitivity,[status(thm)],[64,61]) ).
tff(66,plain,
mult(mult(mult(mult(c,a),b),mult(c,a)),unit) = mult(mult(unit,mult(mult(c,a),mult(b,mult(c,a)))),unit),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
mult(mult(mult(c,a),b),mult(c,a)) = mult(mult(mult(c,a),b),mult(unit,mult(c,a))),
inference(monotonicity,[status(thm)],[39]) ).
tff(68,plain,
mult(mult(mult(c,a),b),mult(unit,mult(c,a))) = mult(mult(mult(c,a),b),mult(c,a)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(mult(c,a),b),mult(unit,mult(c,a))) = mult(mult(mult(c,a),mult(b,unit)),mult(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
mult(mult(mult(c,a),b),mult(unit,mult(c,a))) = mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),
inference(unit_resolution,[status(thm)],[69,48]) ).
tff(71,plain,
mult(mult(mult(c,a),mult(b,unit)),mult(c,a)) = mult(mult(mult(c,a),b),mult(unit,mult(c,a))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
mult(mult(mult(c,a),mult(b,unit)),mult(c,a)) = mult(mult(mult(c,a),b),mult(c,a)),
inference(transitivity,[status(thm)],[71,68]) ).
tff(73,plain,
mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),unit) = mult(mult(mult(mult(c,a),b),mult(c,a)),unit),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),unit) = mult(mult(mult(c,a),mult(b,unit)),mult(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),unit) = mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),
inference(unit_resolution,[status(thm)],[74,26]) ).
tff(76,plain,
mult(mult(mult(c,a),mult(b,unit)),mult(c,a)) = mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),unit),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
^ [B: $i,A: $i] :
refl(
( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
tff(81,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),a),a) = mult(mult(mult(c,a),mult(b,unit)),mult(c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
rd(mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),a),a) = mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),a) = mult(mult(mult(mult(c,a),b),mult(c,a)),a),
inference(monotonicity,[status(thm)],[72]) ).
tff(87,plain,
mult(mult(mult(mult(c,a),b),mult(c,a)),a) = mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),a),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(mult(c,a),b),mult(unit,mult(c,a))) = mult(mult(c,a),mult(mult(b,unit),mult(c,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
mult(mult(mult(c,a),b),mult(unit,mult(c,a))) = mult(mult(c,a),mult(mult(b,unit),mult(c,a))),
inference(unit_resolution,[status(thm)],[88,16]) ).
tff(90,plain,
mult(mult(c,a),mult(mult(b,unit),mult(c,a))) = mult(mult(mult(c,a),b),mult(unit,mult(c,a))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
mult(mult(c,a),mult(mult(b,unit),mult(c,a))) = mult(mult(mult(c,a),b),mult(c,a)),
inference(transitivity,[status(thm)],[90,68]) ).
tff(92,plain,
mult(mult(mult(c,a),mult(mult(b,unit),mult(c,a))),a) = mult(mult(mult(mult(c,a),b),mult(c,a)),a),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(c,mult(a,mult(mult(mult(b,unit),mult(c,a)),a))) = mult(mult(mult(c,a),mult(mult(b,unit),mult(c,a))),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
mult(c,mult(a,mult(mult(mult(b,unit),mult(c,a)),a))) = mult(mult(mult(c,a),mult(mult(b,unit),mult(c,a))),a),
inference(unit_resolution,[status(thm)],[93,58]) ).
tff(95,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(b,unit) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
mult(b,unit) = b,
inference(unit_resolution,[status(thm)],[95,26]) ).
tff(97,plain,
mult(mult(b,unit),mult(c,a)) = mult(b,mult(c,a)),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
mult(b,mult(c,a)) = mult(mult(b,unit),mult(c,a)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
mult(mult(b,mult(c,a)),a) = mult(mult(mult(b,unit),mult(c,a)),a),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
mult(a,mult(mult(b,mult(c,a)),a)) = mult(a,mult(mult(mult(b,unit),mult(c,a)),a)),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(a,b),mult(mult(c,a),a)) = mult(a,mult(mult(b,mult(c,a)),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
mult(mult(a,b),mult(mult(c,a),a)) = mult(a,mult(mult(b,mult(c,a)),a)),
inference(unit_resolution,[status(thm)],[101,16]) ).
tff(103,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(c,a),unit) = mult(c,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
mult(mult(c,a),unit) = mult(c,a),
inference(unit_resolution,[status(thm)],[103,26]) ).
tff(105,plain,
mult(mult(mult(c,a),unit),a) = mult(mult(c,a),a),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(c,mult(a,mult(unit,a))) = mult(mult(mult(c,a),unit),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
mult(c,mult(a,mult(unit,a))) = mult(mult(mult(c,a),unit),a),
inference(unit_resolution,[status(thm)],[106,58]) ).
tff(108,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
mult(unit,a) = a,
inference(unit_resolution,[status(thm)],[108,36]) ).
tff(110,plain,
mult(a,mult(unit,a)) = mult(a,a),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
mult(a,a) = mult(a,mult(unit,a)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
mult(c,mult(a,a)) = mult(c,mult(a,mult(unit,a))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
mult(c,mult(a,a)) = mult(mult(c,a),a),
inference(transitivity,[status(thm)],[112,107,105]) ).
tff(114,plain,
mult(mult(a,b),mult(c,mult(a,a))) = mult(mult(a,b),mult(mult(c,a),a)),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
mult(mult(a,b),mult(c,mult(a,a))) = mult(a,mult(mult(mult(b,unit),mult(c,a)),a)),
inference(transitivity,[status(thm)],[114,102,100]) ).
tff(116,plain,
mult(c,mult(mult(a,b),mult(c,mult(a,a)))) = mult(c,mult(a,mult(mult(mult(b,unit),mult(c,a)),a))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) )
<=> ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) ) )),
inference(bind,[status(th)],]) ).
tff(118,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
tff(121,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) )
| ( mult(c,mult(mult(a,b),mult(c,mult(a,a)))) = mult(mult(mult(c,mult(a,b)),c),mult(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
mult(c,mult(mult(a,b),mult(c,mult(a,a)))) = mult(mult(mult(c,mult(a,b)),c),mult(a,a)),
inference(unit_resolution,[status(thm)],[124,123]) ).
tff(126,plain,
mult(mult(mult(c,mult(a,b)),c),mult(a,a)) = mult(c,mult(mult(a,b),mult(c,mult(a,a)))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
mult(mult(mult(c,mult(a,b)),c),mult(a,mult(unit,a))) = mult(mult(mult(c,mult(a,b)),c),mult(a,a)),
inference(monotonicity,[status(thm)],[110]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(mult(mult(c,mult(a,b)),c),mult(a,mult(unit,a))) = mult(mult(mult(mult(mult(c,mult(a,b)),c),a),unit),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
mult(mult(mult(c,mult(a,b)),c),mult(a,mult(unit,a))) = mult(mult(mult(mult(mult(c,mult(a,b)),c),a),unit),a),
inference(unit_resolution,[status(thm)],[128,58]) ).
tff(130,plain,
mult(mult(mult(mult(mult(c,mult(a,b)),c),a),unit),a) = mult(mult(mult(c,mult(a,b)),c),mult(a,mult(unit,a))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
mult(mult(mult(mult(mult(c,mult(a,b)),c),a),unit),a) = mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),a),
inference(transitivity,[status(thm)],[130,127,126,116,94,92,87]) ).
tff(132,plain,
rd(mult(mult(mult(mult(mult(c,mult(a,b)),c),a),unit),a),a) = rd(mult(mult(mult(mult(c,a),mult(b,unit)),mult(c,a)),a),a),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(mult(c,mult(a,b)),c),a),unit),a),a) = mult(mult(mult(mult(c,mult(a,b)),c),a),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
rd(mult(mult(mult(mult(mult(c,mult(a,b)),c),a),unit),a),a) = mult(mult(mult(mult(c,mult(a,b)),c),a),unit),
inference(unit_resolution,[status(thm)],[133,83]) ).
tff(135,plain,
mult(mult(mult(mult(c,mult(a,b)),c),a),unit) = rd(mult(mult(mult(mult(mult(c,mult(a,b)),c),a),unit),a),a),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(mult(mult(c,mult(a,b)),c),a),unit) = mult(mult(mult(c,mult(a,b)),c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
mult(mult(mult(mult(c,mult(a,b)),c),a),unit) = mult(mult(mult(c,mult(a,b)),c),a),
inference(unit_resolution,[status(thm)],[136,26]) ).
tff(138,plain,
mult(mult(mult(c,mult(a,b)),c),a) = mult(mult(mult(mult(c,mult(a,b)),c),a),unit),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) )
| ( mult(c,mult(mult(a,b),mult(c,a))) = mult(mult(mult(c,mult(a,b)),c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
mult(c,mult(mult(a,b),mult(c,a))) = mult(mult(mult(c,mult(a,b)),c),a),
inference(unit_resolution,[status(thm)],[139,123]) ).
tff(141,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(a,b),mult(c,a)) = mult(mult(a,mult(b,c)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
mult(mult(a,b),mult(c,a)) = mult(mult(a,mult(b,c)),a),
inference(unit_resolution,[status(thm)],[141,48]) ).
tff(143,plain,
mult(mult(a,mult(b,c)),a) = mult(mult(a,b),mult(c,a)),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
mult(c,mult(mult(a,mult(b,c)),a)) = mult(c,mult(mult(a,b),mult(c,a))),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
mult(c,mult(mult(a,mult(b,c)),a)) = mult(mult(c,a),mult(b,mult(c,a))),
inference(transitivity,[status(thm)],[144,140,138,135,132,85,76,73,66,51,41]) ).
tff(146,plain,
mult(mult(c,mult(mult(a,mult(b,c)),a)),b) = mult(mult(mult(c,a),mult(b,mult(c,a))),b),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
mult(b,mult(mult(c,mult(mult(a,mult(b,c)),a)),b)) = mult(b,mult(mult(mult(c,a),mult(b,mult(c,a))),b)),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
mult(b,mult(mult(mult(c,a),mult(b,mult(c,a))),b)) = mult(b,mult(mult(c,mult(mult(a,mult(b,c)),a)),b)),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
mult(mult(mult(c,mult(a,b)),c),a) = mult(mult(c,a),mult(b,mult(c,a))),
inference(transitivity,[status(thm)],[138,135,132,85,76,73,66,51,41]) ).
tff(150,plain,
mult(mult(mult(mult(c,mult(a,b)),c),a),b) = mult(mult(mult(c,a),mult(b,mult(c,a))),b),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
mult(b,mult(mult(mult(mult(c,mult(a,b)),c),a),b)) = mult(b,mult(mult(mult(c,a),mult(b,mult(c,a))),b)),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(b,mult(mult(c,mult(a,b)),c)),mult(a,b)) = mult(b,mult(mult(mult(mult(c,mult(a,b)),c),a),b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
mult(mult(b,mult(mult(c,mult(a,b)),c)),mult(a,b)) = mult(b,mult(mult(mult(mult(c,mult(a,b)),c),a),b)),
inference(unit_resolution,[status(thm)],[152,16]) ).
tff(154,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(a,b),unit) = mult(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
mult(mult(a,b),unit) = mult(a,b),
inference(unit_resolution,[status(thm)],[154,26]) ).
tff(156,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(mult(a,b),unit)) = mult(mult(a,b),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
mult(unit,mult(mult(a,b),unit)) = mult(mult(a,b),unit),
inference(unit_resolution,[status(thm)],[156,36]) ).
tff(158,plain,
mult(unit,mult(mult(a,b),unit)) = mult(a,b),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,plain,
mult(c,mult(unit,mult(mult(a,b),unit))) = mult(c,mult(a,b)),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(c,mult(unit,mult(mult(a,b),unit))) = mult(mult(mult(c,unit),mult(a,b)),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
mult(c,mult(unit,mult(mult(a,b),unit))) = mult(mult(mult(c,unit),mult(a,b)),unit),
inference(unit_resolution,[status(thm)],[160,58]) ).
tff(162,plain,
mult(mult(mult(c,unit),mult(a,b)),unit) = mult(c,mult(unit,mult(mult(a,b),unit))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(c,unit) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
mult(c,unit) = c,
inference(unit_resolution,[status(thm)],[163,26]) ).
tff(165,plain,
mult(mult(c,unit),mult(a,b)) = mult(c,mult(a,b)),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
mult(c,mult(a,b)) = mult(mult(c,unit),mult(a,b)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
mult(mult(c,mult(a,b)),unit) = mult(mult(mult(c,unit),mult(a,b)),unit),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
mult(a,b) = mult(mult(a,b),unit),
inference(symmetry,[status(thm)],[155]) ).
tff(169,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,c) = c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
mult(unit,c) = c,
inference(unit_resolution,[status(thm)],[169,36]) ).
tff(171,plain,
c = mult(unit,c),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
mult(c,mult(a,b)) = mult(mult(unit,c),mult(mult(a,b),unit)),
inference(monotonicity,[status(thm)],[171,168]) ).
tff(173,plain,
mult(mult(unit,c),mult(mult(a,b),unit)) = mult(c,mult(a,b)),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(unit,c),mult(mult(a,b),unit)) = mult(mult(unit,mult(c,mult(a,b))),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
mult(mult(unit,c),mult(mult(a,b),unit)) = mult(mult(unit,mult(c,mult(a,b))),unit),
inference(unit_resolution,[status(thm)],[174,48]) ).
tff(176,plain,
mult(mult(unit,mult(c,mult(a,b))),unit) = mult(mult(unit,c),mult(mult(a,b),unit)),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
mult(mult(unit,mult(c,mult(a,b))),unit) = mult(c,mult(a,b)),
inference(transitivity,[status(thm)],[176,173]) ).
tff(178,plain,
mult(mult(mult(unit,mult(c,mult(a,b))),unit),unit) = mult(mult(c,mult(a,b)),unit),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
mult(mult(mult(unit,mult(c,mult(a,b))),unit),unit) = mult(c,mult(a,b)),
inference(transitivity,[status(thm)],[178,167,162,159]) ).
tff(180,plain,
mult(mult(mult(mult(unit,mult(c,mult(a,b))),unit),unit),c) = mult(mult(c,mult(a,b)),c),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
mult(mult(c,mult(a,b)),c) = mult(mult(mult(mult(unit,mult(c,mult(a,b))),unit),unit),c),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
mult(mult(mult(c,mult(a,b)),c),unit) = mult(mult(mult(mult(mult(unit,mult(c,mult(a,b))),unit),unit),c),unit),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
mult(mult(mult(mult(mult(unit,mult(c,mult(a,b))),unit),unit),c),unit) = mult(mult(mult(c,mult(a,b)),c),unit),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(mult(mult(unit,mult(c,mult(a,b))),unit),mult(unit,mult(c,unit))) = mult(mult(mult(mult(mult(unit,mult(c,mult(a,b))),unit),unit),c),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
mult(mult(mult(unit,mult(c,mult(a,b))),unit),mult(unit,mult(c,unit))) = mult(mult(mult(mult(mult(unit,mult(c,mult(a,b))),unit),unit),c),unit),
inference(unit_resolution,[status(thm)],[184,58]) ).
tff(186,plain,
mult(unit,mult(unit,c)) = mult(unit,c),
inference(monotonicity,[status(thm)],[170]) ).
tff(187,plain,
mult(unit,mult(unit,c)) = c,
inference(transitivity,[status(thm)],[186,170]) ).
tff(188,plain,
mult(mult(unit,mult(unit,c)),unit) = mult(c,unit),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(unit,unit),mult(c,unit)) = mult(mult(unit,mult(unit,c)),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
mult(mult(unit,unit),mult(c,unit)) = mult(mult(unit,mult(unit,c)),unit),
inference(unit_resolution,[status(thm)],[189,48]) ).
tff(191,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,unit) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
mult(unit,unit) = unit,
inference(unit_resolution,[status(thm)],[191,36]) ).
tff(193,plain,
unit = mult(unit,unit),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
mult(unit,mult(c,unit)) = mult(mult(unit,unit),mult(c,unit)),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
mult(unit,mult(c,unit)) = c,
inference(transitivity,[status(thm)],[194,190,188,164]) ).
tff(196,plain,
mult(mult(mult(unit,mult(c,mult(a,b))),unit),mult(unit,mult(c,unit))) = mult(mult(c,mult(a,b)),c),
inference(monotonicity,[status(thm)],[177,195]) ).
tff(197,plain,
mult(mult(c,mult(a,b)),c) = mult(mult(mult(unit,mult(c,mult(a,b))),unit),mult(unit,mult(c,unit))),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
mult(mult(c,mult(a,b)),c) = mult(mult(mult(c,mult(a,b)),c),unit),
inference(transitivity,[status(thm)],[197,185,183]) ).
tff(199,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(200,plain,
mult(unit,b) = b,
inference(unit_resolution,[status(thm)],[199,36]) ).
tff(201,plain,
b = mult(unit,b),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
mult(b,mult(mult(c,mult(a,b)),c)) = mult(mult(unit,b),mult(mult(mult(c,mult(a,b)),c),unit)),
inference(monotonicity,[status(thm)],[201,198]) ).
tff(203,plain,
mult(mult(unit,b),mult(mult(mult(c,mult(a,b)),c),unit)) = mult(b,mult(mult(c,mult(a,b)),c)),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(unit,b),mult(mult(mult(c,mult(a,b)),c),unit)) = mult(mult(unit,mult(b,mult(mult(c,mult(a,b)),c))),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
mult(mult(unit,b),mult(mult(mult(c,mult(a,b)),c),unit)) = mult(mult(unit,mult(b,mult(mult(c,mult(a,b)),c))),unit),
inference(unit_resolution,[status(thm)],[204,48]) ).
tff(206,plain,
mult(mult(unit,mult(b,mult(mult(c,mult(a,b)),c))),unit) = mult(mult(unit,b),mult(mult(mult(c,mult(a,b)),c),unit)),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
mult(mult(unit,mult(b,mult(mult(c,mult(a,b)),c))),unit) = mult(b,mult(mult(c,mult(a,b)),c)),
inference(transitivity,[status(thm)],[206,203]) ).
tff(208,plain,
mult(mult(mult(unit,mult(b,mult(mult(c,mult(a,b)),c))),unit),mult(a,b)) = mult(mult(b,mult(mult(c,mult(a,b)),c)),mult(a,b)),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
mult(mult(c,mult(a,b)),mult(unit,c)) = mult(mult(c,mult(a,b)),c),
inference(monotonicity,[status(thm)],[170]) ).
tff(210,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(c,mult(a,b)),mult(unit,c)) = mult(c,mult(mult(mult(a,b),unit),c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(211,plain,
mult(mult(c,mult(a,b)),mult(unit,c)) = mult(c,mult(mult(mult(a,b),unit),c)),
inference(unit_resolution,[status(thm)],[210,16]) ).
tff(212,plain,
mult(c,mult(mult(mult(a,b),unit),c)) = mult(mult(c,mult(a,b)),mult(unit,c)),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
mult(mult(mult(a,b),unit),c) = mult(mult(a,b),mult(unit,c)),
inference(monotonicity,[status(thm)],[155,171]) ).
tff(214,plain,
mult(mult(a,b),mult(unit,c)) = mult(mult(mult(a,b),unit),c),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
mult(mult(a,b),c) = mult(mult(a,b),mult(unit,c)),
inference(monotonicity,[status(thm)],[171]) ).
tff(216,plain,
mult(mult(a,b),c) = mult(mult(mult(a,b),unit),c),
inference(transitivity,[status(thm)],[215,214]) ).
tff(217,plain,
mult(mult(c,unit),mult(mult(a,b),c)) = mult(c,mult(mult(mult(a,b),unit),c)),
inference(monotonicity,[status(thm)],[164,216]) ).
tff(218,plain,
c = mult(c,unit),
inference(symmetry,[status(thm)],[164]) ).
tff(219,plain,
mult(c,mult(mult(a,b),c)) = mult(mult(c,unit),mult(mult(a,b),c)),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
mult(c,mult(mult(a,b),c)) = mult(mult(c,mult(a,b)),c),
inference(transitivity,[status(thm)],[219,217,212,209]) ).
tff(221,plain,
mult(b,mult(c,mult(mult(a,b),c))) = mult(b,mult(mult(c,mult(a,b)),c)),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(b,mult(c,mult(mult(a,b),c))) = mult(mult(mult(b,c),mult(a,b)),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
mult(b,mult(c,mult(mult(a,b),c))) = mult(mult(mult(b,c),mult(a,b)),c),
inference(unit_resolution,[status(thm)],[222,58]) ).
tff(224,plain,
mult(mult(mult(b,c),mult(a,b)),c) = mult(b,mult(c,mult(mult(a,b),c))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
mult(mult(mult(b,c),mult(a,b)),c) = mult(mult(unit,mult(b,mult(mult(c,mult(a,b)),c))),unit),
inference(transitivity,[status(thm)],[224,221,202,205]) ).
tff(226,plain,
mult(mult(mult(mult(b,c),mult(a,b)),c),mult(a,b)) = mult(mult(mult(unit,mult(b,mult(mult(c,mult(a,b)),c))),unit),mult(a,b)),
inference(monotonicity,[status(thm)],[225]) ).
tff(227,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(mult(b,c),mult(mult(a,b),mult(c,mult(a,b)))) = mult(mult(mult(mult(b,c),mult(a,b)),c),mult(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
mult(mult(b,c),mult(mult(a,b),mult(c,mult(a,b)))) = mult(mult(mult(mult(b,c),mult(a,b)),c),mult(a,b)),
inference(unit_resolution,[status(thm)],[227,58]) ).
tff(229,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(unit,a),mult(b,unit)) = mult(mult(unit,mult(a,b)),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(230,plain,
mult(mult(unit,a),mult(b,unit)) = mult(mult(unit,mult(a,b)),unit),
inference(unit_resolution,[status(thm)],[229,48]) ).
tff(231,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(unit,a),mult(b,unit)) = mult(unit,mult(mult(a,b),unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
mult(mult(unit,a),mult(b,unit)) = mult(unit,mult(mult(a,b),unit)),
inference(unit_resolution,[status(thm)],[231,16]) ).
tff(233,plain,
mult(unit,mult(mult(a,b),unit)) = mult(mult(unit,a),mult(b,unit)),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
mult(mult(a,b),unit) = mult(unit,mult(mult(a,b),unit)),
inference(symmetry,[status(thm)],[157]) ).
tff(235,plain,
mult(a,b) = mult(mult(unit,mult(a,b)),unit),
inference(transitivity,[status(thm)],[168,234,233,230]) ).
tff(236,plain,
mult(mult(a,b),mult(c,mult(a,b))) = mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))) = mult(mult(a,b),mult(c,mult(a,b))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
mult(mult(b,c),mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b)))) = mult(mult(b,c),mult(mult(a,b),mult(c,mult(a,b)))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
mult(mult(b,c),mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b)))) = mult(mult(b,c),mult(mult(mult(a,mult(b,c)),a),b)),
inference(transitivity,[status(thm)],[238,228,226,208,153,151,148,19]) ).
tff(240,plain,
ld(mult(b,c),mult(mult(b,c),mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))))) = ld(mult(b,c),mult(mult(b,c),mult(mult(mult(a,mult(b,c)),a),b))),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(b,c),mult(mult(b,c),mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))))) = mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(242,plain,
ld(mult(b,c),mult(mult(b,c),mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))))) = mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))),
inference(unit_resolution,[status(thm)],[241,7]) ).
tff(243,plain,
mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))) = ld(mult(b,c),mult(mult(b,c),mult(mult(mult(unit,mult(a,b)),unit),mult(c,mult(a,b))))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
mult(mult(a,b),mult(c,mult(a,b))) = mult(mult(mult(a,mult(b,c)),a),b),
inference(transitivity,[status(thm)],[236,243,240,9]) ).
tff(245,plain,
( ( mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b) )
<=> ( mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(246,axiom,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(247,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
$false,
inference(unit_resolution,[status(thm)],[247,244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP669-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 19:46:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------