TSTP Solution File: ALG245-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG245-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 Sep 6 16:09:31 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 31
% Syntax : Number of formulae : 94 ( 68 unt; 5 typ; 0 def)
% Number of atoms : 118 ( 113 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 41 ( 16 ~; 12 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 166 ( 152 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) )
<=> ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) )
| ( mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) )
<=> ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
tff(15,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) )
| ( mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))) = mult(mult(a,c),mult(b,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))) = mult(mult(a,c),mult(b,d)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(a,c),mult(b,d))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(a,c),mult(b,d))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d)))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) )
| ( mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(a,c),mult(b,d))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(a,c),mult(b,d))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
inference(unit_resolution,[status(thm)],[22,7]) ).
tff(24,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d))),mult(mult(a,c),mult(b,d))),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) )
| ( mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,c),mult(b,d))) = mult(mult(a,b),mult(c,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,c),mult(b,d))) = mult(mult(a,b),mult(c,d)),
inference(unit_resolution,[status(thm)],[25,17]) ).
tff(27,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) )
<=> ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
tff(33,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) )
| ( mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) = mult(mult(a,c),mult(b,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) = mult(mult(a,c),mult(b,d)),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
mult(mult(a,c),mult(b,d)) = mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
mult(mult(a,c),mult(b,d)) = mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),
inference(transitivity,[status(thm)],[38,28,24,21,10]) ).
tff(40,plain,
mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))) = mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))) = mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) )
| ( mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))) = mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))) = mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) )
<=> ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
tff(49,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) )
| ( mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,c),mult(b,d))),
inference(monotonicity,[status(thm)],[37]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) )
| ( mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))),
inference(unit_resolution,[status(thm)],[56,51]) ).
tff(58,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))) = mult(mult(a,b),mult(c,d)),
inference(transitivity,[status(thm)],[57,55,26]) ).
tff(59,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))) = mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))),
inference(transitivity,[status(thm)],[9,20,23,27,60,54]) ).
tff(62,plain,
mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) )
| ( mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),
inference(unit_resolution,[status(thm)],[64,51]) ).
tff(66,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),
inference(monotonicity,[status(thm)],[37]) ).
tff(68,plain,
mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) )
| ( mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),
inference(unit_resolution,[status(thm)],[69,51]) ).
tff(71,plain,
mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) )
| ( mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))) = mult(mult(a,b),mult(c,d)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))) = mult(mult(a,b),mult(c,d)),
inference(unit_resolution,[status(thm)],[72,35]) ).
tff(74,plain,
mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))) = mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))) = mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
mult(mult(a,c),mult(b,d)) = mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))),
inference(symmetry,[status(thm)],[19]) ).
tff(77,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))) = mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),
inference(transitivity,[status(thm)],[53,59,37,76,75,71,68,66]) ).
tff(78,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,c),mult(b,d)),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),mult(mult(a,c),mult(b,d)))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) )
| ( mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d)))),
inference(unit_resolution,[status(thm)],[80,51]) ).
tff(82,plain,
mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d))) = mult(mult(a,c),mult(b,d)),
inference(transitivity,[status(thm)],[9,20,23,27,37]) ).
tff(83,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d)))) = mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) = mult(mult(mult(a,b),mult(c,d)),mult(mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),mult(mult(a,b),mult(c,d)))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) = mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
inference(transitivity,[status(thm)],[84,81,79,63,44,41]) ).
tff(86,plain,
( ( mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))) )
<=> ( mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(88,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
$false,
inference(unit_resolution,[status(thm)],[88,85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG245-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.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 : Mon Aug 29 14:54:50 EDT 2022
% 0.12/0.34 % 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.
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------