%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG245-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 04:58:50 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 73 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 98 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 14 ~; 10 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 159 ( 144 !; 0 ?; 159 :)
% 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,
^ [A: $i] :
refl(( ( mult(A,A) = A )
<=> ( mult(A,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i] : ( mult(A,A) = A )
<=> ! [A: $i] : ( mult(A,A) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( mult(A,A) = A )
<=> ! [A: $i] : ( mult(A,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: $i] : ( mult(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
tff(5,plain,
! [A: $i] : ( mult(A,A) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( mult(A,A) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( mult(A,A) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( mult(A,A) = A )
| ( 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(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(9,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(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)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,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(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(a,b),mult(c,d)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
mult(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,c),mult(b,d)),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)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,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(23,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)],[22,21]) ).
tff(24,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)],[23]) ).
tff(25,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)],[24,20]) ).
tff(26,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(27,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)],[26,25]) ).
tff(28,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)],[27]) ).
tff(29,plain,
mult(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(a,b),mult(c,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)],[28]) ).
tff(30,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(a,b),mult(c,d)))) = mult(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)],[29]) ).
tff(31,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(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(a,b),mult(c,d)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,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(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(a,b),mult(c,d)))),
inference(unit_resolution,[status(thm)],[31,16]) ).
tff(33,plain,
( ~ ! [A: $i] : ( mult(A,A) = A )
| ( mult(mult(mult(a,c),mult(b,d)),mult(mult(a,c),mult(b,d))) = mult(mult(a,c),mult(b,d)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
mult(mult(mult(a,c),mult(b,d)),mult(mult(a,c),mult(b,d))) = mult(mult(a,c),mult(b,d)),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,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(a,c),mult(b,d))) = mult(mult(mult(a,c),mult(b,d)),mult(mult(a,c),mult(b,d))),
inference(monotonicity,[status(thm)],[27]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,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(40,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) )
| ( 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(a,c),mult(b,d))) = mult(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(quant_inst,[status(thm)],[]) ).
tff(44,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(a,c),mult(b,d))) = mult(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(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
mult(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)))) = 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(a,c),mult(b,d))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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(49,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(50,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)],[49,48]) ).
tff(51,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)],[50]) ).
tff(52,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)],[51,47]) ).
tff(53,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(54,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)],[53,52]) ).
tff(55,plain,
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))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
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,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)],[55]) ).
tff(57,plain,
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(transitivity,[status(thm)],[56,45,35,34]) ).
tff(58,plain,
( ~ ! [A: $i] : ( mult(A,A) = A )
| ( mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d))) = mult(mult(a,b),mult(c,d)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d))) = mult(mult(a,b),mult(c,d)),
inference(unit_resolution,[status(thm)],[58,7]) ).
tff(60,plain,
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)],[59]) ).
tff(61,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(a,b),mult(c,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,c),mult(b,d))),
inference(monotonicity,[status(thm)],[60,57]) ).
tff(62,plain,
mult(mult(mult(mult(a,b),mult(c,d)),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,b),mult(c,d)),mult(mult(a,c),mult(b,d))),mult(mult(a,b),mult(c,d)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) )
| ( mult(mult(mult(mult(a,b),mult(c,d)),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(a,c),mult(b,d)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
mult(mult(mult(mult(a,b),mult(c,d)),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(a,c),mult(b,d)))),
inference(unit_resolution,[status(thm)],[63,42]) ).
tff(65,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(a,c),mult(b,d)))) = mult(mult(mult(mult(a,b),mult(c,d)),mult(mult(a,b),mult(c,d))),mult(mult(a,c),mult(b,d))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [A: $i] : ( mult(A,A) = A )
| ( 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(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(67,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(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)],[66,7]) ).
tff(68,plain,
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(a,c),mult(b,d)))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,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)],[68,65,62,32,30,18,9]) ).
tff(70,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(71,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(72,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)],[71,70]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ALG245-1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 : Thu Jun 19 11:00:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------