%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP702-12 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:08:30 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 45
% Syntax : Number of formulae : 128 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 171 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 67 ( 23 ~; 19 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 8 ( 8 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 172 ( 157 !; 0 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(op_d_type,type,
op_d: $i ).
tff(x0_type,type,
x0: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(op_c_type,type,
op_c: $i ).
tff(op_f_type,type,
op_f: $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',f04) ).
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(x0,op_d),x1),ld(mult(mult(x0,op_d),x1),op_c)),ld(mult(mult(x0,op_d),x1),op_c)) = mult(mult(x0,op_d),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
rd(mult(mult(mult(x0,op_d),x1),ld(mult(mult(x0,op_d),x1),op_c)),ld(mult(mult(x0,op_d),x1),op_c)) = mult(mult(x0,op_d),x1),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i] :
refl(( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
tff(14,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(op_d,x1),mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c))) = ld(mult(x0,mult(op_d,x1)),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ld(mult(op_d,x1),mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c))) = ld(mult(x0,mult(op_d,x1)),op_c),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x0,mult(x0,mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c)))) = mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
ld(x0,mult(x0,mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c)))) = mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c)),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
^ [B: $i,A: $i] :
refl(( ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
<=> ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
<=> ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
<=> ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f13) ).
tff(25,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
| ( op_f = mult(x0,mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
op_f = mult(x0,mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
| ( op_f = mult(x0,mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
op_f = mult(x0,mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c))),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
mult(x0,mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c))) = op_f,
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
mult(x0,mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c))) = mult(x0,mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c))),
inference(transitivity,[status(thm)],[32,29]) ).
tff(34,plain,
ld(x0,mult(x0,mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c)))) = ld(x0,mult(x0,mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c)))),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(x0,mult(x0,mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c)))) = mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
ld(x0,mult(x0,mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c)))) = mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c)),
inference(unit_resolution,[status(thm)],[35,16]) ).
tff(37,plain,
mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c)) = ld(x0,mult(x0,mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c)))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
<=> ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
tff(42,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
| ( mult(x0,mult(op_d,op_c)) = mult(mult(x0,op_d),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
mult(x0,mult(op_d,op_c)) = mult(mult(x0,op_d),op_c),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
ld(mult(x0,mult(op_d,op_c)),op_c) = ld(mult(mult(x0,op_d),op_c),op_c),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
ld(mult(mult(x0,op_d),op_c),op_c) = ld(mult(x0,mult(op_d,op_c)),op_c),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
mult(mult(op_d,op_c),ld(mult(mult(x0,op_d),op_c),op_c)) = mult(mult(op_d,op_c),ld(mult(x0,mult(op_d,op_c)),op_c)),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
tff(54,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
| ( mult(op_d,mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))) = mult(mult(op_d,op_c),ld(mult(mult(x0,op_d),op_c),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
mult(op_d,mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))) = mult(mult(op_d,op_c),ld(mult(mult(x0,op_d),op_c),op_c)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
^ [A: $i] :
refl(( ( op_d = ld(A,mult(op_c,A)) )
<=> ( op_d = ld(A,mult(op_c,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) )
<=> ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) )
<=> ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
tff(63,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) )
| ( op_d = ld(op_c,mult(op_c,op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
ld(op_c,mult(op_c,op_c)) = op_d,
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,op_c)) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(unit_resolution,[status(thm)],[69,16]) ).
tff(71,plain,
op_c = ld(op_c,mult(op_c,op_c)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
op_c = op_d,
inference(transitivity,[status(thm)],[71,68]) ).
tff(73,plain,
mult(op_c,mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))) = mult(op_d,mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(x0,op_d),mult(mult(x0,op_d),mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c)))) = mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
ld(mult(x0,op_d),mult(mult(x0,op_d),mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c)))) = mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c)),
inference(unit_resolution,[status(thm)],[74,16]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
| ( op_f = mult(mult(x0,op_d),mult(x1,ld(mult(mult(x0,op_d),x1),op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
op_f = mult(mult(x0,op_d),mult(x1,ld(mult(mult(x0,op_d),x1),op_c))),
inference(unit_resolution,[status(thm)],[76,27]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
| ( op_f = mult(mult(x0,op_d),mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
op_f = mult(mult(x0,op_d),mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))),
inference(unit_resolution,[status(thm)],[78,27]) ).
tff(80,plain,
mult(mult(x0,op_d),mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))) = op_f,
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
mult(mult(x0,op_d),mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))) = mult(mult(x0,op_d),mult(x1,ld(mult(mult(x0,op_d),x1),op_c))),
inference(transitivity,[status(thm)],[80,77]) ).
tff(82,plain,
ld(mult(x0,op_d),mult(mult(x0,op_d),mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c)))) = ld(mult(x0,op_d),mult(mult(x0,op_d),mult(x1,ld(mult(mult(x0,op_d),x1),op_c)))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
ld(mult(x0,op_d),mult(mult(x0,op_d),mult(x1,ld(mult(mult(x0,op_d),x1),op_c)))) = ld(mult(x0,op_d),mult(mult(x0,op_d),mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c)))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(x0,op_d),mult(mult(x0,op_d),mult(x1,ld(mult(mult(x0,op_d),x1),op_c)))) = mult(x1,ld(mult(mult(x0,op_d),x1),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
ld(mult(x0,op_d),mult(mult(x0,op_d),mult(x1,ld(mult(mult(x0,op_d),x1),op_c)))) = mult(x1,ld(mult(mult(x0,op_d),x1),op_c)),
inference(unit_resolution,[status(thm)],[84,16]) ).
tff(86,plain,
mult(x1,ld(mult(mult(x0,op_d),x1),op_c)) = ld(mult(x0,op_d),mult(mult(x0,op_d),mult(x1,ld(mult(mult(x0,op_d),x1),op_c)))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
mult(x1,ld(mult(mult(x0,op_d),x1),op_c)) = mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c)),
inference(transitivity,[status(thm)],[86,83,75]) ).
tff(88,plain,
mult(op_c,mult(x1,ld(mult(mult(x0,op_d),x1),op_c))) = mult(op_c,mult(op_c,ld(mult(mult(x0,op_d),op_c),op_c))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
^ [B: $i,A: $i] :
refl(( ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
<=> ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
<=> ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
<=> ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
tff(93,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
| ( mult(op_c,mult(x1,ld(mult(mult(x0,op_d),x1),op_c))) = mult(mult(op_c,x1),ld(mult(mult(x0,op_d),x1),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
mult(op_c,mult(x1,ld(mult(mult(x0,op_d),x1),op_c))) = mult(mult(op_c,x1),ld(mult(mult(x0,op_d),x1),op_c)),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
mult(mult(op_c,x1),ld(mult(mult(x0,op_d),x1),op_c)) = mult(op_c,mult(x1,ld(mult(mult(x0,op_d),x1),op_c))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
mult(mult(op_c,x1),ld(mult(mult(x0,op_d),x1),op_c)) = mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c)),
inference(transitivity,[status(thm)],[98,88,73,58,49,37,34,20]) ).
tff(100,plain,
mult(op_c,x1) = mult(op_d,x1),
inference(monotonicity,[status(thm)],[72]) ).
tff(101,plain,
ld(mult(op_c,x1),mult(mult(op_c,x1),ld(mult(mult(x0,op_d),x1),op_c))) = ld(mult(op_d,x1),mult(mult(op_d,x1),ld(mult(x0,mult(op_d,x1)),op_c))),
inference(monotonicity,[status(thm)],[100,99]) ).
tff(102,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(op_c,x1),mult(mult(op_c,x1),ld(mult(mult(x0,op_d),x1),op_c))) = ld(mult(mult(x0,op_d),x1),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
ld(mult(op_c,x1),mult(mult(op_c,x1),ld(mult(mult(x0,op_d),x1),op_c))) = ld(mult(mult(x0,op_d),x1),op_c),
inference(unit_resolution,[status(thm)],[102,16]) ).
tff(104,plain,
ld(mult(mult(x0,op_d),x1),op_c) = ld(mult(op_c,x1),mult(mult(op_c,x1),ld(mult(mult(x0,op_d),x1),op_c))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
ld(mult(mult(x0,op_d),x1),op_c) = ld(mult(x0,mult(op_d,x1)),op_c),
inference(transitivity,[status(thm)],[104,101,18]) ).
tff(106,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,ld(A,B)) = B )
<=> ( mult(A,ld(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
tff(110,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)) = op_c,
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
op_c = mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(mult(mult(x0,op_d),x1),ld(mult(mult(x0,op_d),x1),op_c)) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
mult(mult(mult(x0,op_d),x1),ld(mult(mult(x0,op_d),x1),op_c)) = op_c,
inference(unit_resolution,[status(thm)],[116,112]) ).
tff(118,plain,
mult(mult(mult(x0,op_d),x1),ld(mult(mult(x0,op_d),x1),op_c)) = mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
rd(mult(mult(mult(x0,op_d),x1),ld(mult(mult(x0,op_d),x1),op_c)),ld(mult(mult(x0,op_d),x1),op_c)) = rd(mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)),ld(mult(x0,mult(op_d,x1)),op_c)),
inference(monotonicity,[status(thm)],[118,105]) ).
tff(120,plain,
rd(mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)),ld(mult(x0,mult(op_d,x1)),op_c)) = rd(mult(mult(mult(x0,op_d),x1),ld(mult(mult(x0,op_d),x1),op_c)),ld(mult(mult(x0,op_d),x1),op_c)),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)),ld(mult(x0,mult(op_d,x1)),op_c)) = mult(x0,mult(op_d,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
rd(mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)),ld(mult(x0,mult(op_d,x1)),op_c)) = mult(x0,mult(op_d,x1)),
inference(unit_resolution,[status(thm)],[121,7]) ).
tff(123,plain,
mult(x0,mult(op_d,x1)) = rd(mult(mult(x0,mult(op_d,x1)),ld(mult(x0,mult(op_d,x1)),op_c)),ld(mult(x0,mult(op_d,x1)),op_c)),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
mult(x0,mult(op_d,x1)) = mult(mult(x0,op_d),x1),
inference(transitivity,[status(thm)],[123,120,9]) ).
tff(125,plain,
( ( mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1) )
<=> ( mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,axiom,
mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(127,plain,
mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP702-12 : TPTP v9.0.0. Released v8.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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 16:58:01 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.55 % SZS status Unsatisfiable
% 0.20/0.55 % SZS output start Proof
% See solution above
% 0.20/0.56 % E exiting
%------------------------------------------------------------------------------