%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP669-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:08:26 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 40
% Syntax : Number of formulae : 130 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 168 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 63 ( 24 ~; 20 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 6 ( 6 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 200 ( 184 !; 0 ?; 200 :)
% 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(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
tff(5,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(a,mult(b,c)),a),b),mult(c,a)),mult(c,a)) = mult(mult(mult(a,mult(b,c)),a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
rd(mult(mult(mult(mult(a,mult(b,c)),a),b),mult(c,a)),mult(c,a)) = 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(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(11,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)],[10]) ).
tff(12,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(13,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(14,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)],[13,12]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) )
| ( mult(mult(a,b),mult(c,mult(mult(a,b),mult(c,a)))) = mult(mult(mult(mult(a,b),c),mult(a,b)),mult(c,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
mult(mult(a,b),mult(c,mult(mult(a,b),mult(c,a)))) = mult(mult(mult(mult(a,b),c),mult(a,b)),mult(c,a)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,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(23,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)],[22,21]) ).
tff(24,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)],[23]) ).
tff(25,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)],[24,20]) ).
tff(26,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(27,plain,
mult(mult(a,b),mult(c,a)) = mult(mult(a,mult(b,c)),a),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
mult(c,mult(mult(a,b),mult(c,a))) = mult(c,mult(mult(a,mult(b,c)),a)),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
mult(mult(a,b),mult(c,mult(mult(a,b),mult(c,a)))) = mult(mult(a,b),mult(c,mult(mult(a,mult(b,c)),a))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
mult(mult(a,b),mult(c,mult(mult(a,mult(b,c)),a))) = mult(mult(a,b),mult(c,mult(mult(a,b),mult(c,a)))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34,33]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36,32]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(c,a),mult(b,c)) = mult(c,mult(mult(a,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
mult(mult(c,a),mult(b,c)) = mult(c,mult(mult(a,b),c)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
mult(c,mult(mult(a,b),c)) = mult(mult(c,a),mult(b,c)),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
mult(mult(c,mult(mult(a,b),c)),a) = mult(mult(mult(c,a),mult(b,c)),a),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
mult(mult(mult(c,a),mult(b,c)),a) = mult(mult(c,mult(mult(a,b),c)),a),
inference(symmetry,[status(thm)],[41]) ).
tff(43,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(44,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)],[43]) ).
tff(45,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(46,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(47,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)],[46,45]) ).
tff(48,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)],[47]) ).
tff(49,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)],[48,44]) ).
tff(50,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(b,c),a))) = mult(mult(mult(c,a),mult(b,c)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
mult(c,mult(a,mult(mult(b,c),a))) = mult(mult(mult(c,a),mult(b,c)),a),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,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(c,a)) = mult(a,mult(mult(b,c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
mult(mult(a,b),mult(c,a)) = mult(a,mult(mult(b,c),a)),
inference(unit_resolution,[status(thm)],[52,37]) ).
tff(54,plain,
mult(a,mult(mult(b,c),a)) = mult(mult(a,b),mult(c,a)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
mult(a,mult(mult(b,c),a)) = mult(mult(a,mult(b,c)),a),
inference(transitivity,[status(thm)],[54,27]) ).
tff(56,plain,
mult(c,mult(a,mult(mult(b,c),a))) = mult(c,mult(mult(a,mult(b,c)),a)),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
mult(c,mult(mult(a,mult(b,c)),a)) = mult(c,mult(a,mult(mult(b,c),a))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
mult(c,mult(mult(a,mult(b,c)),a)) = mult(mult(c,mult(mult(a,b),c)),a),
inference(transitivity,[status(thm)],[57,51,42]) ).
tff(59,plain,
mult(mult(a,b),mult(c,mult(mult(a,mult(b,c)),a))) = mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),a)),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),a)) = mult(mult(a,b),mult(c,mult(mult(a,mult(b,c)),a))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,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,mult(mult(a,b),c)),a)) = mult(a,mult(mult(b,mult(c,mult(mult(a,b),c))),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),a)) = mult(a,mult(mult(b,mult(c,mult(mult(a,b),c))),a)),
inference(unit_resolution,[status(thm)],[61,37]) ).
tff(63,plain,
mult(a,mult(mult(b,mult(c,mult(mult(a,b),c))),a)) = mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),a)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(a,b)) = mult(b,mult(mult(c,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
mult(mult(b,c),mult(a,b)) = mult(b,mult(mult(c,a),b)),
inference(unit_resolution,[status(thm)],[64,37]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(b,c),mult(a,b)) = mult(mult(b,mult(c,a)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
mult(mult(b,c),mult(a,b)) = mult(mult(b,mult(c,a)),b),
inference(unit_resolution,[status(thm)],[66,25]) ).
tff(68,plain,
mult(mult(b,mult(c,a)),b) = mult(mult(b,c),mult(a,b)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
mult(mult(b,mult(c,a)),b) = mult(b,mult(mult(c,a),b)),
inference(transitivity,[status(thm)],[68,65]) ).
tff(70,plain,
mult(mult(mult(b,mult(c,a)),b),c) = mult(mult(b,mult(mult(c,a),b)),c),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) )
| ( mult(b,mult(mult(c,a),mult(b,c))) = mult(mult(mult(b,mult(c,a)),b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
mult(b,mult(mult(c,a),mult(b,c))) = mult(mult(mult(b,mult(c,a)),b),c),
inference(unit_resolution,[status(thm)],[71,16]) ).
tff(73,plain,
mult(b,mult(c,mult(mult(a,b),c))) = mult(b,mult(mult(c,a),mult(b,c))),
inference(monotonicity,[status(thm)],[40]) ).
tff(74,plain,
mult(b,mult(c,mult(mult(a,b),c))) = mult(mult(b,mult(mult(c,a),b)),c),
inference(transitivity,[status(thm)],[73,72,70]) ).
tff(75,plain,
mult(mult(b,mult(c,mult(mult(a,b),c))),a) = mult(mult(mult(b,mult(mult(c,a),b)),c),a),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
mult(a,mult(mult(b,mult(c,mult(mult(a,b),c))),a)) = mult(a,mult(mult(mult(b,mult(mult(c,a),b)),c),a)),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
mult(a,mult(mult(mult(b,mult(mult(c,a),b)),c),a)) = mult(a,mult(mult(b,mult(c,mult(mult(a,b),c))),a)),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(a,mult(b,mult(mult(c,a),b))),mult(c,a)) = mult(a,mult(mult(mult(b,mult(mult(c,a),b)),c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
mult(mult(a,mult(b,mult(mult(c,a),b))),mult(c,a)) = mult(a,mult(mult(mult(b,mult(mult(c,a),b)),c),a)),
inference(unit_resolution,[status(thm)],[78,37]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(a,mult(b,mult(mult(c,a),b))) = mult(mult(mult(a,b),mult(c,a)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
mult(a,mult(b,mult(mult(c,a),b))) = mult(mult(mult(a,b),mult(c,a)),b),
inference(unit_resolution,[status(thm)],[80,49]) ).
tff(82,plain,
mult(mult(mult(a,b),mult(c,a)),b) = mult(a,mult(b,mult(mult(c,a),b))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
mult(mult(mult(a,b),mult(c,a)),b) = mult(mult(mult(a,mult(b,c)),a),b),
inference(monotonicity,[status(thm)],[27]) ).
tff(84,plain,
mult(mult(mult(a,mult(b,c)),a),b) = mult(mult(mult(a,b),mult(c,a)),b),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
mult(mult(mult(a,mult(b,c)),a),b) = mult(a,mult(b,mult(mult(c,a),b))),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
mult(mult(mult(mult(a,mult(b,c)),a),b),mult(c,a)) = mult(mult(a,mult(b,mult(mult(c,a),b))),mult(c,a)),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
mult(mult(mult(mult(a,mult(b,c)),a),b),mult(c,a)) = mult(mult(mult(mult(a,b),c),mult(a,b)),mult(c,a)),
inference(transitivity,[status(thm)],[86,79,77,63,60,30,18]) ).
tff(88,plain,
rd(mult(mult(mult(mult(a,mult(b,c)),a),b),mult(c,a)),mult(c,a)) = rd(mult(mult(mult(mult(a,b),c),mult(a,b)),mult(c,a)),mult(c,a)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
rd(mult(mult(mult(mult(a,b),c),mult(a,b)),mult(c,a)),mult(c,a)) = rd(mult(mult(mult(mult(a,mult(b,c)),a),b),mult(c,a)),mult(c,a)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(mult(a,b),c),mult(a,b)),mult(c,a)),mult(c,a)) = mult(mult(mult(a,b),c),mult(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
rd(mult(mult(mult(mult(a,b),c),mult(a,b)),mult(c,a)),mult(c,a)) = mult(mult(mult(a,b),c),mult(a,b)),
inference(unit_resolution,[status(thm)],[90,7]) ).
tff(92,plain,
mult(mult(mult(a,b),c),mult(a,b)) = rd(mult(mult(mult(mult(a,b),c),mult(a,b)),mult(c,a)),mult(c,a)),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
^ [B: $i,A: $i] :
refl(( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(94,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)],[93]) ).
tff(95,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(96,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
tff(97,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(a,b)))) = mult(mult(mult(a,b),c),mult(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
ld(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(a,b)))) = mult(mult(mult(a,b),c),mult(a,b)),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(a,b))) = mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),mult(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
mult(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(a,b))) = mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),mult(a,b))),
inference(unit_resolution,[status(thm)],[102,37]) ).
tff(104,plain,
mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),mult(a,b))) = mult(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(a,b))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
mult(mult(c,mult(mult(a,b),c)),mult(a,b)) = mult(mult(mult(c,a),mult(b,c)),mult(a,b)),
inference(monotonicity,[status(thm)],[40]) ).
tff(106,plain,
mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),mult(a,b))) = mult(mult(a,b),mult(mult(mult(c,a),mult(b,c)),mult(a,b))),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
mult(mult(a,b),mult(mult(mult(c,a),mult(b,c)),mult(a,b))) = mult(mult(a,b),mult(mult(c,mult(mult(a,b),c)),mult(a,b))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) )
| ( mult(mult(mult(a,b),mult(c,a)),mult(mult(b,c),mult(a,b))) = mult(mult(a,b),mult(mult(mult(c,a),mult(b,c)),mult(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
mult(mult(mult(a,b),mult(c,a)),mult(mult(b,c),mult(a,b))) = mult(mult(a,b),mult(mult(mult(c,a),mult(b,c)),mult(a,b))),
inference(unit_resolution,[status(thm)],[108,37]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A) )
| ( mult(mult(mult(a,b),mult(c,a)),mult(mult(b,c),mult(a,b))) = mult(mult(mult(a,b),mult(mult(c,a),mult(b,c))),mult(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
mult(mult(mult(a,b),mult(c,a)),mult(mult(b,c),mult(a,b))) = mult(mult(mult(a,b),mult(mult(c,a),mult(b,c))),mult(a,b)),
inference(unit_resolution,[status(thm)],[110,25]) ).
tff(112,plain,
mult(mult(mult(a,b),mult(mult(c,a),mult(b,c))),mult(a,b)) = mult(mult(mult(a,b),mult(c,a)),mult(mult(b,c),mult(a,b))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
mult(mult(a,b),mult(c,mult(mult(a,b),c))) = mult(mult(a,b),mult(mult(c,a),mult(b,c))),
inference(monotonicity,[status(thm)],[40]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) )
| ( mult(mult(a,b),mult(c,mult(mult(a,b),c))) = mult(mult(mult(mult(a,b),c),mult(a,b)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
mult(mult(a,b),mult(c,mult(mult(a,b),c))) = mult(mult(mult(mult(a,b),c),mult(a,b)),c),
inference(unit_resolution,[status(thm)],[114,16]) ).
tff(116,plain,
mult(mult(mult(mult(a,b),c),mult(a,b)),c) = mult(mult(a,b),mult(c,mult(mult(a,b),c))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
mult(mult(mult(mult(a,b),c),mult(a,b)),c) = mult(mult(a,b),mult(mult(c,a),mult(b,c))),
inference(transitivity,[status(thm)],[116,113]) ).
tff(118,plain,
mult(mult(mult(mult(mult(a,b),c),mult(a,b)),c),mult(a,b)) = mult(mult(mult(a,b),mult(mult(c,a),mult(b,c))),mult(a,b)),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) )
| ( mult(mult(mult(a,b),c),mult(mult(a,b),mult(c,mult(a,b)))) = mult(mult(mult(mult(mult(a,b),c),mult(a,b)),c),mult(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
mult(mult(mult(a,b),c),mult(mult(a,b),mult(c,mult(a,b)))) = mult(mult(mult(mult(mult(a,b),c),mult(a,b)),c),mult(a,b)),
inference(unit_resolution,[status(thm)],[119,49]) ).
tff(121,plain,
mult(mult(mult(a,b),c),mult(mult(a,b),mult(c,mult(a,b)))) = mult(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(a,b))),
inference(transitivity,[status(thm)],[120,118,112,109,107,104]) ).
tff(122,plain,
ld(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(mult(a,b),mult(c,mult(a,b))))) = ld(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(a,b)))),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(mult(a,b),mult(c,mult(a,b))))) = mult(mult(a,b),mult(c,mult(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
ld(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(mult(a,b),mult(c,mult(a,b))))) = mult(mult(a,b),mult(c,mult(a,b))),
inference(unit_resolution,[status(thm)],[123,99]) ).
tff(125,plain,
mult(mult(a,b),mult(c,mult(a,b))) = ld(mult(mult(a,b),c),mult(mult(mult(a,b),c),mult(mult(a,b),mult(c,mult(a,b))))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
mult(mult(a,b),mult(c,mult(a,b))) = mult(mult(mult(a,mult(b,c)),a),b),
inference(transitivity,[status(thm)],[125,122,101,92,89,9]) ).
tff(127,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(128,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(129,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
$false,
inference(unit_resolution,[status(thm)],[129,126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP669-1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 16:50:17 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------