%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP703-12 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.59s 0.78s
% Output : Proof 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 57
% Syntax : Number of formulae : 182 ( 136 unt; 0 typ; 0 def)
% Number of atoms : 248 ( 237 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 85 ( 29 ~; 25 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 10 ( 10 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 218 ( 199 !; 0 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x3_type,type,
x3: $i ).
tff(op_e_type,type,
op_e: $i ).
tff(x2_type,type,
x2: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(op_c_type,type,
op_c: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(op_d_type,type,
op_d: $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/sandbox2/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(x2,op_e),x3),op_c),op_c) = mult(mult(x2,op_e),x3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
rd(mult(mult(mult(x2,op_e),x3),op_c),op_c) = mult(mult(x2,op_e),x3),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
tff(14,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
| ( mult(op_c,mult(x2,mult(op_e,x3))) = mult(mult(op_c,x2),mult(op_e,x3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
mult(op_c,mult(x2,mult(op_e,x3))) = mult(mult(op_c,x2),mult(op_e,x3)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
mult(mult(op_c,x2),mult(op_e,x3)) = mult(op_c,mult(x2,mult(op_e,x3))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
ld(mult(x2,mult(op_e,x3)),mult(mult(op_c,x2),mult(op_e,x3))) = ld(mult(x2,mult(op_e,x3)),mult(op_c,mult(x2,mult(op_e,x3)))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
ld(mult(x2,mult(op_e,x3)),mult(op_c,mult(x2,mult(op_e,x3)))) = ld(mult(x2,mult(op_e,x3)),mult(mult(op_c,x2),mult(op_e,x3))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,axiom,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
tff(26,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [A: $i] : ( op_d = ld(A,mult(op_c,A)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) )
| ( op_d = ld(mult(x2,mult(op_e,x3)),mult(op_c,mult(x2,mult(op_e,x3)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
op_d = ld(mult(x2,mult(op_e,x3)),mult(op_c,mult(x2,mult(op_e,x3)))),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,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(32,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[31,28]) ).
tff(33,plain,
ld(op_c,mult(op_c,op_c)) = op_d,
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [B: $i,A: $i] :
refl(( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(35,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)],[34]) ).
tff(36,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(37,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
tff(38,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,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(42,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
op_c = ld(op_c,mult(op_c,op_c)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
op_c = ld(mult(x2,mult(op_e,x3)),mult(mult(op_c,x2),mult(op_e,x3))),
inference(transitivity,[status(thm)],[43,33,30,21]) ).
tff(45,plain,
mult(mult(x2,mult(op_e,x3)),op_c) = mult(mult(x2,mult(op_e,x3)),ld(mult(x2,mult(op_e,x3)),mult(mult(op_c,x2),mult(op_e,x3)))),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
mult(mult(x2,mult(op_e,x3)),ld(mult(x2,mult(op_e,x3)),mult(mult(op_c,x2),mult(op_e,x3)))) = mult(mult(x2,mult(op_e,x3)),op_c),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,ld(A,B)) = B )
<=> ( mult(A,ld(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(48,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)],[47]) ).
tff(49,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(50,axiom,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
tff(51,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(mult(x2,mult(op_e,x3)),ld(mult(x2,mult(op_e,x3)),mult(mult(op_c,x2),mult(op_e,x3)))) = mult(mult(op_c,x2),mult(op_e,x3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
mult(mult(x2,mult(op_e,x3)),ld(mult(x2,mult(op_e,x3)),mult(mult(op_c,x2),mult(op_e,x3)))) = mult(mult(op_c,x2),mult(op_e,x3)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
mult(mult(op_c,x2),mult(op_e,x3)) = mult(mult(x2,mult(op_e,x3)),ld(mult(x2,mult(op_e,x3)),mult(mult(op_c,x2),mult(op_e,x3)))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,axiom,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f13) ).
tff(61,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
| ( op_f = mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
op_f = mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c))),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
| ( op_f = mult(mult(op_e,x3),mult(op_c,ld(mult(mult(op_e,x3),op_c),op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
op_f = mult(mult(op_e,x3),mult(op_c,ld(mult(mult(op_e,x3),op_c),op_c))),
inference(unit_resolution,[status(thm)],[66,63]) ).
tff(68,plain,
mult(mult(op_e,x3),mult(op_c,ld(mult(mult(op_e,x3),op_c),op_c))) = op_f,
inference(symmetry,[status(thm)],[67]) ).
tff(69,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(70,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)],[69]) ).
tff(71,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(72,axiom,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
tff(73,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
| ( mult(mult(op_e,x3),mult(op_c,ld(mult(mult(op_e,x3),op_c),op_c))) = mult(mult(mult(op_e,x3),op_c),ld(mult(mult(op_e,x3),op_c),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
mult(mult(op_e,x3),mult(op_c,ld(mult(mult(op_e,x3),op_c),op_c))) = mult(mult(mult(op_e,x3),op_c),ld(mult(mult(op_e,x3),op_c),op_c)),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
mult(mult(mult(op_e,x3),op_c),ld(mult(mult(op_e,x3),op_c),op_c)) = mult(mult(op_e,x3),mult(op_c,ld(mult(mult(op_e,x3),op_c),op_c))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(mult(mult(op_e,x3),op_c),ld(mult(mult(op_e,x3),op_c),op_c)) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
mult(mult(mult(op_e,x3),op_c),ld(mult(mult(op_e,x3),op_c),op_c)) = op_c,
inference(unit_resolution,[status(thm)],[79,53]) ).
tff(81,plain,
op_c = mult(mult(mult(op_e,x3),op_c),ld(mult(mult(op_e,x3),op_c),op_c)),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
op_c = mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c))),
inference(transitivity,[status(thm)],[81,78,68,65]) ).
tff(83,plain,
ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c) = ld(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
ld(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)))) = ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)))) = mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
ld(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)))) = mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)),
inference(unit_resolution,[status(thm)],[85,40]) ).
tff(87,plain,
mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)) = ld(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
^ [B: $i,A: $i] :
refl(( ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
<=> ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
<=> ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
<=> ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f12) ).
tff(92,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
| ( op_e = mult(mult(rd(op_c,mult(x2,mult(op_e,x3))),mult(op_e,x3)),x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
op_e = mult(mult(rd(op_c,mult(x2,mult(op_e,x3))),mult(op_e,x3)),x2),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
| ( op_e = mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
op_e = mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),
inference(unit_resolution,[status(thm)],[97,94]) ).
tff(99,plain,
mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e) = op_e,
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e) = mult(mult(rd(op_c,mult(x2,mult(op_e,x3))),mult(op_e,x3)),x2),
inference(transitivity,[status(thm)],[99,96]) ).
tff(101,plain,
ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),op_c) = ld(mult(mult(rd(op_c,mult(x2,mult(op_e,x3))),mult(op_e,x3)),x2),op_c),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
ld(mult(mult(rd(op_c,mult(x2,mult(op_e,x3))),mult(op_e,x3)),x2),op_c) = ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),op_c),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)) = mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),
inference(monotonicity,[status(thm)],[99]) ).
tff(104,plain,
mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)) = mult(mult(rd(op_c,mult(x2,mult(op_e,x3))),mult(op_e,x3)),x2),
inference(transitivity,[status(thm)],[103,99,96]) ).
tff(105,plain,
ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c) = ld(mult(mult(rd(op_c,mult(x2,mult(op_e,x3))),mult(op_e,x3)),x2),op_c),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c) = ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),op_c),
inference(transitivity,[status(thm)],[105,102]) ).
tff(107,plain,
mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)) = mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),op_c)),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),op_c)) = mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e)),op_c)),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),op_c)) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),op_c)) = op_c,
inference(unit_resolution,[status(thm)],[109,53]) ).
tff(111,plain,
op_c = mult(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),ld(mult(mult(rd(op_c,mult(op_e,x3)),x3),op_e),op_c)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
op_c = ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c),
inference(transitivity,[status(thm)],[111,108,87,84]) ).
tff(113,plain,
mult(x3,op_c) = mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c)),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c)) = mult(x3,op_c),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c)))) = mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c)))) = mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c)),
inference(unit_resolution,[status(thm)],[115,40]) ).
tff(117,plain,
^ [B: $i,A: $i] :
refl(( ( mult(rd(A,B),B) = A )
<=> ( mult(rd(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,axiom,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
tff(121,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3)) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3)) = op_c,
inference(unit_resolution,[status(thm)],[124,123]) ).
tff(126,plain,
op_c = mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3)),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
| ( op_f = mult(rd(op_c,mult(op_e,x3)),mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
op_f = mult(rd(op_c,mult(op_e,x3)),mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c))),
inference(unit_resolution,[status(thm)],[127,63]) ).
tff(129,plain,
mult(rd(op_c,mult(op_e,x3)),mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c))) = op_f,
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
mult(rd(op_c,mult(op_e,x3)),mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c))) = mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3)),
inference(transitivity,[status(thm)],[129,67,77,80,126]) ).
tff(131,plain,
ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c)))) = ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3))),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3))) = ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(x3,ld(mult(rd(op_c,mult(op_e,x3)),x3),op_c)))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3))) = mult(op_e,x3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3))) = mult(op_e,x3),
inference(unit_resolution,[status(thm)],[133,40]) ).
tff(135,plain,
mult(op_e,x3) = ld(rd(op_c,mult(op_e,x3)),mult(rd(op_c,mult(op_e,x3)),mult(op_e,x3))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
mult(op_e,x3) = mult(x3,op_c),
inference(transitivity,[status(thm)],[135,132,116,114]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
| ( op_e = mult(mult(rd(op_c,mult(op_c,x2)),x2),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
op_e = mult(mult(rd(op_c,mult(op_c,x2)),x2),op_c),
inference(unit_resolution,[status(thm)],[137,94]) ).
tff(139,plain,
mult(mult(rd(op_c,mult(op_c,x2)),x2),op_c) = op_e,
inference(symmetry,[status(thm)],[138]) ).
tff(140,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(141,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)],[140]) ).
tff(142,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(143,axiom,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
tff(144,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
| ( mult(rd(op_c,mult(op_c,x2)),mult(x2,op_c)) = mult(mult(rd(op_c,mult(op_c,x2)),x2),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
mult(rd(op_c,mult(op_c,x2)),mult(x2,op_c)) = mult(mult(rd(op_c,mult(op_c,x2)),x2),op_c),
inference(unit_resolution,[status(thm)],[147,146]) ).
tff(149,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(x2,ld(x2,mult(op_c,x2))) = mult(op_c,x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
mult(x2,ld(x2,mult(op_c,x2))) = mult(op_c,x2),
inference(unit_resolution,[status(thm)],[149,53]) ).
tff(151,plain,
( ~ ! [A: $i] : ( op_d = ld(A,mult(op_c,A)) )
| ( op_d = ld(x2,mult(op_c,x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
op_d = ld(x2,mult(op_c,x2)),
inference(unit_resolution,[status(thm)],[151,28]) ).
tff(153,plain,
ld(x2,mult(op_c,x2)) = op_d,
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
ld(x2,mult(op_c,x2)) = op_c,
inference(transitivity,[status(thm)],[153,32,42]) ).
tff(155,plain,
mult(x2,ld(x2,mult(op_c,x2))) = mult(x2,op_c),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
mult(x2,op_c) = mult(x2,ld(x2,mult(op_c,x2))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
mult(x2,op_c) = mult(op_c,x2),
inference(transitivity,[status(thm)],[156,150]) ).
tff(158,plain,
mult(rd(op_c,mult(op_c,x2)),mult(x2,op_c)) = mult(rd(op_c,mult(op_c,x2)),mult(op_c,x2)),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
mult(rd(op_c,mult(op_c,x2)),mult(op_c,x2)) = mult(rd(op_c,mult(op_c,x2)),mult(x2,op_c)),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(op_c,mult(op_c,x2)),mult(op_c,x2)) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
mult(rd(op_c,mult(op_c,x2)),mult(op_c,x2)) = op_c,
inference(unit_resolution,[status(thm)],[160,123]) ).
tff(162,plain,
op_c = mult(rd(op_c,mult(op_c,x2)),mult(op_c,x2)),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
op_c = op_e,
inference(transitivity,[status(thm)],[162,159,148,139]) ).
tff(164,plain,
mult(x2,op_c) = mult(x2,op_e),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
mult(op_c,x2) = mult(x2,ld(x2,mult(op_c,x2))),
inference(symmetry,[status(thm)],[150]) ).
tff(166,plain,
mult(op_c,x2) = mult(x2,op_e),
inference(transitivity,[status(thm)],[165,155,164]) ).
tff(167,plain,
mult(mult(op_c,x2),mult(op_e,x3)) = mult(mult(x2,op_e),mult(x3,op_c)),
inference(monotonicity,[status(thm)],[166,136]) ).
tff(168,plain,
mult(mult(x2,op_e),mult(x3,op_c)) = mult(mult(op_c,x2),mult(op_e,x3)),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
| ( mult(mult(x2,op_e),mult(x3,op_c)) = mult(mult(mult(x2,op_e),x3),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
mult(mult(x2,op_e),mult(x3,op_c)) = mult(mult(mult(x2,op_e),x3),op_c),
inference(unit_resolution,[status(thm)],[169,146]) ).
tff(171,plain,
mult(mult(mult(x2,op_e),x3),op_c) = mult(mult(x2,op_e),mult(x3,op_c)),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
mult(mult(mult(x2,op_e),x3),op_c) = mult(mult(x2,mult(op_e,x3)),op_c),
inference(transitivity,[status(thm)],[171,168,56,46]) ).
tff(173,plain,
rd(mult(mult(mult(x2,op_e),x3),op_c),op_c) = rd(mult(mult(x2,mult(op_e,x3)),op_c),op_c),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
rd(mult(mult(x2,mult(op_e,x3)),op_c),op_c) = rd(mult(mult(mult(x2,op_e),x3),op_c),op_c),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(x2,mult(op_e,x3)),op_c),op_c) = mult(x2,mult(op_e,x3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
rd(mult(mult(x2,mult(op_e,x3)),op_c),op_c) = mult(x2,mult(op_e,x3)),
inference(unit_resolution,[status(thm)],[175,7]) ).
tff(177,plain,
mult(x2,mult(op_e,x3)) = rd(mult(mult(x2,mult(op_e,x3)),op_c),op_c),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
mult(x2,mult(op_e,x3)) = mult(mult(x2,op_e),x3),
inference(transitivity,[status(thm)],[177,174,9]) ).
tff(179,plain,
( ( mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3) )
<=> ( mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,axiom,
mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(181,plain,
mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
$false,
inference(unit_resolution,[status(thm)],[181,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP703-12 : TPTP v9.0.0. Released v8.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % 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 16:56:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.59/0.78 % SZS status Unsatisfiable
% 0.59/0.78 % SZS output start Proof
% See solution above
% 0.59/0.80 % E exiting
%------------------------------------------------------------------------------