%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP728-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:08:33 AM UTC 2025
% Result : Unsatisfiable 268.62s 268.92s
% Output : Proof 268.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 73
% Syntax : Number of formulae : 243 ( 181 unt; 0 typ; 0 def)
% Number of atoms : 325 ( 314 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 117 ( 45 ~; 41 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 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 : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 288 ( 265 !; 0 ?; 288 :)
% Comments :
%------------------------------------------------------------------------------
tff(unit_type,type,
unit: $i ).
tff(op_k_type,type,
op_k: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(asoc_type,type,
asoc: ( $i * $i * $i ) > $i ).
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(i_type,type,
i: $i > $i ).
tff(1,plain,
^ [B: $i,D: $i,A: $i,E: $i,C: $i] :
refl(( ( asoc(A,B,asoc(C,D,E)) = unit )
<=> ( asoc(A,B,asoc(C,D,E)) = unit ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c22) ).
tff(5,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(A,B,asoc(C,D,E)) = unit )
| ( asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = unit,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
tff(14,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
mult(unit,asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [B: $i,A: $i] :
refl(( ( mult(i(A),mult(A,B)) = B )
<=> ( mult(i(A),mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
tff(23,plain,
! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(op_k(a,b)),mult(op_k(a,b),c)) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
mult(i(op_k(a,b)),mult(op_k(a,b),c)) = c,
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
<=> ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
<=> ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
<=> ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c11) ).
tff(32,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
| ( mult(op_k(a,b),c) = mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
mult(op_k(a,b),c) = mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)) = mult(op_k(a,b),c),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(i(op_k(a,b)),mult(op_k(a,b),c)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = c,
inference(transitivity,[status(thm)],[38,27]) ).
tff(40,plain,
mult(i(c),mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = mult(i(c),c),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
mult(i(c),c) = mult(i(c),mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [A: $i] :
refl(( ( mult(i(A),A) = unit )
<=> ( mult(i(A),A) = unit ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [A: $i] : ( mult(i(A),A) = unit )
<=> ! [A: $i] : ( mult(i(A),A) = unit ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [A: $i] : ( mult(i(A),A) = unit )
<=> ! [A: $i] : ( mult(i(A),A) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [A: $i] : ( mult(i(A),A) = unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
tff(46,plain,
! [A: $i] : ( mult(i(A),A) = unit ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [A: $i] : ( mult(i(A),A) = unit ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [A: $i] : ( mult(i(A),A) = unit ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [A: $i] : ( mult(i(A),A) = unit )
| ( mult(i(c),c) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
mult(i(c),c) = unit,
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
unit = mult(i(c),c),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
unit = mult(i(c),mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(transitivity,[status(thm)],[51,41]) ).
tff(53,plain,
mult(unit,asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = mult(mult(i(c),mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
mult(mult(i(c),mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = mult(unit,asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
<=> ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
tff(59,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
| ( mult(mult(i(c),i(op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(mult(i(c),mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
mult(mult(i(c),i(op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(mult(i(c),mult(i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
^ [B: $i,A: $i] :
refl(( ( i(mult(A,B)) = mult(i(A),i(B)) )
<=> ( i(mult(A,B)) = mult(i(A),i(B)) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
<=> ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
<=> ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
tff(68,plain,
! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
| ( i(mult(c,op_k(a,b))) = mult(i(c),i(op_k(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
i(mult(c,op_k(a,b))) = mult(i(c),i(op_k(a,b))),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
mult(i(c),i(op_k(a,b))) = i(mult(c,op_k(a,b))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
mult(mult(i(c),i(op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(i(mult(c,op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
mult(i(mult(c,op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(mult(i(c),i(op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(mult(c,op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = op_k(op_k(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
mult(i(mult(c,op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = op_k(op_k(a,b),c),
inference(unit_resolution,[status(thm)],[76,25]) ).
tff(78,plain,
op_k(op_k(a,b),c) = mult(i(mult(c,op_k(a,b))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
op_k(op_k(a,b),c) = asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(transitivity,[status(thm)],[78,75,63,54,18]) ).
tff(80,plain,
asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c)) = asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),asoc(i(c),i(op_k(a,b)),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
mult(unit,asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c)),
inference(unit_resolution,[status(thm)],[81,16]) ).
tff(83,plain,
( ~ ! [A: $i] : ( mult(i(A),A) = unit )
| ( mult(i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
mult(i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = unit,
inference(unit_resolution,[status(thm)],[83,48]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
| ( i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),
inference(unit_resolution,[status(thm)],[85,70]) ).
tff(87,plain,
mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))) = i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = unit,
inference(transitivity,[status(thm)],[88,84]) ).
tff(90,plain,
mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(unit,asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c)),
inference(transitivity,[status(thm)],[90,82]) ).
tff(92,plain,
mult(i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(symmetry,[status(thm)],[88]) ).
tff(93,plain,
unit = mult(i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(symmetry,[status(thm)],[84]) ).
tff(94,plain,
^ [B: $i,D: $i,A: $i,E: $i,C: $i] :
refl(( ( asoc(asoc(A,B,C),D,E) = unit )
<=> ( asoc(asoc(A,B,C),D,E) = unit ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit )
<=> ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21) ).
tff(98,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [B: $i,D: $i,A: $i,E: $i,C: $i] : ( asoc(asoc(A,B,C),D,E) = unit )
| ( asoc(asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),c)),asoc(i(op_k(a,b)),op_k(a,b),c)),mult(i(c),i(op_k(a,b)))) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
asoc(asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),c)),asoc(i(op_k(a,b)),op_k(a,b),c)),mult(i(c),i(op_k(a,b)))) = unit,
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
| ( mult(mult(i(op_k(a,b)),op_k(a,b)),c) = mult(mult(i(op_k(a,b)),mult(op_k(a,b),c)),asoc(i(op_k(a,b)),op_k(a,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
mult(mult(i(op_k(a,b)),op_k(a,b)),c) = mult(mult(i(op_k(a,b)),mult(op_k(a,b),c)),asoc(i(op_k(a,b)),op_k(a,b),c)),
inference(unit_resolution,[status(thm)],[103,61]) ).
tff(105,plain,
( ~ ! [A: $i] : ( mult(i(A),A) = unit )
| ( mult(i(op_k(a,b)),op_k(a,b)) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
mult(i(op_k(a,b)),op_k(a,b)) = unit,
inference(unit_resolution,[status(thm)],[105,48]) ).
tff(107,plain,
unit = mult(i(op_k(a,b)),op_k(a,b)),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
mult(unit,c) = mult(mult(i(op_k(a,b)),op_k(a,b)),c),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
mult(unit,c) = c,
inference(unit_resolution,[status(thm)],[109,16]) ).
tff(111,plain,
c = mult(unit,c),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(i(c)),mult(i(c),c)) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
mult(i(i(c)),mult(i(c),c)) = c,
inference(unit_resolution,[status(thm)],[112,25]) ).
tff(114,plain,
^ [A: $i] :
refl(( ( mult(A,i(A)) = unit )
<=> ( mult(A,i(A)) = unit ) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [A: $i] : ( mult(A,i(A)) = unit )
<=> ! [A: $i] : ( mult(A,i(A)) = unit ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
( ! [A: $i] : ( mult(A,i(A)) = unit )
<=> ! [A: $i] : ( mult(A,i(A)) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
! [A: $i] : ( mult(A,i(A)) = unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
tff(118,plain,
! [A: $i] : ( mult(A,i(A)) = unit ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [A: $i] : ( mult(A,i(A)) = unit ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [A: $i] : ( mult(A,i(A)) = unit ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
( ~ ! [A: $i] : ( mult(A,i(A)) = unit )
| ( mult(i(c),i(i(c))) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
mult(i(c),i(i(c))) = unit,
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
mult(i(c),i(i(c))) = mult(i(c),c),
inference(transitivity,[status(thm)],[122,51]) ).
tff(124,plain,
mult(i(i(c)),mult(i(c),i(i(c)))) = mult(i(i(c)),mult(i(c),c)),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(i(c)),mult(i(c),i(i(c)))) = i(i(c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
mult(i(i(c)),mult(i(c),i(i(c)))) = i(i(c)),
inference(unit_resolution,[status(thm)],[125,25]) ).
tff(127,plain,
i(i(c)) = mult(i(i(c)),mult(i(c),i(i(c)))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
i(i(c)) = mult(mult(i(op_k(a,b)),mult(op_k(a,b),c)),asoc(i(op_k(a,b)),op_k(a,b),c)),
inference(transitivity,[status(thm)],[127,124,113,111,108,104]) ).
tff(129,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) = asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
mult(unit,asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) = asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),
inference(unit_resolution,[status(thm)],[129,16]) ).
tff(131,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(a),mult(a,b)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
mult(i(a),mult(a,b)) = b,
inference(unit_resolution,[status(thm)],[131,25]) ).
tff(133,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,B) = mult(mult(B,A),op_k(A,B)) )
| ( mult(a,b) = mult(mult(b,a),op_k(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
mult(a,b) = mult(mult(b,a),op_k(a,b)),
inference(unit_resolution,[status(thm)],[133,34]) ).
tff(135,plain,
mult(mult(b,a),op_k(a,b)) = mult(a,b),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
mult(i(a),mult(mult(b,a),op_k(a,b))) = mult(i(a),mult(a,b)),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
mult(i(a),mult(mult(b,a),op_k(a,b))) = b,
inference(transitivity,[status(thm)],[136,132]) ).
tff(138,plain,
mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))) = mult(i(b),b),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
mult(i(b),b) = mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [A: $i] : ( mult(i(A),A) = unit )
| ( mult(i(b),b) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
mult(i(b),b) = unit,
inference(unit_resolution,[status(thm)],[140,48]) ).
tff(142,plain,
unit = mult(i(b),b),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
unit = mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),
inference(transitivity,[status(thm)],[142,139]) ).
tff(144,plain,
mult(unit,asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) = mult(mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
mult(mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) = mult(unit,asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
| ( mult(mult(i(b),i(a)),mult(mult(b,a),op_k(a,b))) = mult(mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
mult(mult(i(b),i(a)),mult(mult(b,a),op_k(a,b))) = mult(mult(i(b),mult(i(a),mult(mult(b,a),op_k(a,b)))),asoc(i(b),i(a),mult(mult(b,a),op_k(a,b)))),
inference(unit_resolution,[status(thm)],[146,61]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
| ( i(mult(b,a)) = mult(i(b),i(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
i(mult(b,a)) = mult(i(b),i(a)),
inference(unit_resolution,[status(thm)],[148,70]) ).
tff(150,plain,
mult(i(b),i(a)) = i(mult(b,a)),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
mult(mult(i(b),i(a)),mult(mult(b,a),op_k(a,b))) = mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))) = mult(mult(i(b),i(a)),mult(mult(b,a),op_k(a,b))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))) = op_k(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))) = op_k(a,b),
inference(unit_resolution,[status(thm)],[153,25]) ).
tff(155,plain,
op_k(a,b) = mult(i(mult(b,a)),mult(mult(b,a),op_k(a,b))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
op_k(a,b) = asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),
inference(transitivity,[status(thm)],[155,152,147,145,130]) ).
tff(157,plain,
asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b)))) = asoc(asoc(i(b),i(a),mult(mult(b,a),op_k(a,b))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),c)),asoc(i(op_k(a,b)),op_k(a,b),c)),mult(i(c),i(op_k(a,b)))),
inference(monotonicity,[status(thm)],[156,128]) ).
tff(158,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b))))) = asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
mult(unit,asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b))))) = asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b)))),
inference(unit_resolution,[status(thm)],[158,16]) ).
tff(160,plain,
( ~ ! [A: $i] : ( mult(A,i(A)) = unit )
| ( mult(op_k(a,b),i(op_k(a,b))) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
mult(op_k(a,b),i(op_k(a,b))) = unit,
inference(unit_resolution,[status(thm)],[160,120]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(i(c)),mult(i(c),i(op_k(a,b)))) = i(op_k(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
mult(i(i(c)),mult(i(c),i(op_k(a,b)))) = i(op_k(a,b)),
inference(unit_resolution,[status(thm)],[162,25]) ).
tff(164,plain,
mult(op_k(a,b),mult(i(i(c)),mult(i(c),i(op_k(a,b))))) = mult(op_k(a,b),i(op_k(a,b))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
mult(op_k(a,b),mult(i(i(c)),mult(i(c),i(op_k(a,b))))) = unit,
inference(transitivity,[status(thm)],[164,161]) ).
tff(166,plain,
mult(mult(op_k(a,b),mult(i(i(c)),mult(i(c),i(op_k(a,b))))),asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b))))) = mult(unit,asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b))))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
| ( mult(mult(op_k(a,b),i(i(c))),mult(i(c),i(op_k(a,b)))) = mult(mult(op_k(a,b),mult(i(i(c)),mult(i(c),i(op_k(a,b))))),asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
mult(mult(op_k(a,b),i(i(c))),mult(i(c),i(op_k(a,b)))) = mult(mult(op_k(a,b),mult(i(i(c)),mult(i(c),i(op_k(a,b))))),asoc(op_k(a,b),i(i(c)),mult(i(c),i(op_k(a,b))))),
inference(unit_resolution,[status(thm)],[167,61]) ).
tff(169,plain,
^ [A: $i] :
refl(( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],[]) ).
tff(170,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
tff(173,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(i(i(op_k(a,b))),unit) = i(i(op_k(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
mult(i(i(op_k(a,b))),unit) = i(i(op_k(a,b))),
inference(unit_resolution,[status(thm)],[176,175]) ).
tff(178,plain,
mult(i(i(op_k(a,b))),unit) = mult(i(i(op_k(a,b))),mult(i(op_k(a,b)),op_k(a,b))),
inference(monotonicity,[status(thm)],[107]) ).
tff(179,plain,
mult(i(i(op_k(a,b))),mult(i(op_k(a,b)),op_k(a,b))) = mult(i(i(op_k(a,b))),unit),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(i(op_k(a,b))),mult(i(op_k(a,b)),op_k(a,b))) = op_k(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
mult(i(i(op_k(a,b))),mult(i(op_k(a,b)),op_k(a,b))) = op_k(a,b),
inference(unit_resolution,[status(thm)],[180,25]) ).
tff(182,plain,
op_k(a,b) = mult(i(i(op_k(a,b))),mult(i(op_k(a,b)),op_k(a,b))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
op_k(a,b) = i(i(op_k(a,b))),
inference(transitivity,[status(thm)],[182,179,177]) ).
tff(184,plain,
mult(op_k(a,b),i(i(c))) = mult(i(i(op_k(a,b))),i(i(c))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
mult(i(i(op_k(a,b))),i(i(c))) = mult(op_k(a,b),i(i(c))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(i(i(op_k(a,b))),i(i(c))),unit) = mult(i(i(op_k(a,b))),i(i(c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
mult(mult(i(i(op_k(a,b))),i(i(c))),unit) = mult(i(i(op_k(a,b))),i(i(c))),
inference(unit_resolution,[status(thm)],[186,175]) ).
tff(188,plain,
unit = mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(transitivity,[status(thm)],[93,92]) ).
tff(189,plain,
( ~ ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
| ( i(mult(op_k(a,b),c)) = mult(i(op_k(a,b)),i(c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
i(mult(op_k(a,b),c)) = mult(i(op_k(a,b)),i(c)),
inference(unit_resolution,[status(thm)],[189,70]) ).
tff(191,plain,
i(mult(op_k(a,b),c)) = i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(monotonicity,[status(thm)],[36]) ).
tff(192,plain,
i(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))) = i(mult(op_k(a,b),c)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))) = mult(i(op_k(a,b)),i(c)),
inference(transitivity,[status(thm)],[87,192,190]) ).
tff(194,plain,
i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))) = i(mult(i(op_k(a,b)),i(c))),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
i(mult(i(op_k(a,b)),i(c))) = i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
| ( i(mult(i(op_k(a,b)),i(c))) = mult(i(i(op_k(a,b))),i(i(c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
i(mult(i(op_k(a,b)),i(c))) = mult(i(i(op_k(a,b))),i(i(c))),
inference(unit_resolution,[status(thm)],[196,70]) ).
tff(198,plain,
mult(i(i(op_k(a,b))),i(i(c))) = i(mult(i(op_k(a,b)),i(c))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
mult(i(i(op_k(a,b))),i(i(c))) = i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),
inference(transitivity,[status(thm)],[198,195]) ).
tff(200,plain,
mult(mult(i(i(op_k(a,b))),i(i(c))),unit) = mult(i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(monotonicity,[status(thm)],[199,188]) ).
tff(201,plain,
mult(i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = mult(mult(i(i(op_k(a,b))),i(i(c))),unit),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
mult(i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),
inference(unit_resolution,[status(thm)],[202,25]) ).
tff(204,plain,
mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)) = mult(i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)) = mult(op_k(a,b),i(i(c))),
inference(transitivity,[status(thm)],[204,201,187,185]) ).
tff(206,plain,
mult(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),mult(i(c),i(op_k(a,b)))) = mult(mult(op_k(a,b),i(i(c))),mult(i(c),i(op_k(a,b)))),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
mult(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),mult(i(c),i(op_k(a,b)))) = mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(transitivity,[status(thm)],[206,168,166,159,157,102,93,92]) ).
tff(208,plain,
mult(mult(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),mult(i(c),i(op_k(a,b)))),mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c)))) = mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(monotonicity,[status(thm)],[207,91]) ).
tff(209,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
| ( mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b))),op_k(op_k(a,b),c)) = mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b))),op_k(op_k(a,b),c)) = mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(unit_resolution,[status(thm)],[209,61]) ).
tff(211,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,op_k(op_k(a,b),c)) = op_k(op_k(a,b),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
mult(unit,op_k(op_k(a,b),c)) = op_k(op_k(a,b),c),
inference(unit_resolution,[status(thm)],[211,16]) ).
tff(213,plain,
mult(unit,op_k(op_k(a,b),c)) = mult(mult(i(op_k(a,b)),op_k(a,b)),op_k(op_k(a,b),c)),
inference(monotonicity,[status(thm)],[107]) ).
tff(214,plain,
mult(mult(i(op_k(a,b)),op_k(a,b)),op_k(op_k(a,b),c)) = mult(unit,op_k(op_k(a,b),c)),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
| ( mult(mult(i(op_k(a,b)),op_k(a,b)),op_k(op_k(a,b),c)) = mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
mult(mult(i(op_k(a,b)),op_k(a,b)),op_k(op_k(a,b),c)) = mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))),
inference(unit_resolution,[status(thm)],[215,61]) ).
tff(217,plain,
mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))) = mult(mult(i(op_k(a,b)),op_k(a,b)),op_k(op_k(a,b),c)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))) = op_k(op_k(a,b),c),
inference(transitivity,[status(thm)],[217,214,212]) ).
tff(219,plain,
mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b))) = mult(mult(i(op_k(a,b)),i(c)),mult(c,op_k(a,b))),
inference(monotonicity,[status(thm)],[193]) ).
tff(220,plain,
mult(mult(i(op_k(a,b)),i(c)),mult(c,op_k(a,b))) = mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) )
| ( mult(mult(i(op_k(a,b)),i(c)),mult(c,op_k(a,b))) = mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
mult(mult(i(op_k(a,b)),i(c)),mult(c,op_k(a,b))) = mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))),
inference(unit_resolution,[status(thm)],[221,61]) ).
tff(223,plain,
mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))) = mult(mult(i(op_k(a,b)),i(c)),mult(c,op_k(a,b))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))) = mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b))),
inference(transitivity,[status(thm)],[223,220]) ).
tff(225,plain,
mult(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c)))) = mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b))),op_k(op_k(a,b),c)),
inference(monotonicity,[status(thm)],[224,218]) ).
tff(226,plain,
mult(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c)))) = mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c))),
inference(transitivity,[status(thm)],[225,210]) ).
tff(227,plain,
mult(i(i(op_k(a,b))),i(i(c))) = mult(mult(i(i(op_k(a,b))),i(i(c))),unit),
inference(symmetry,[status(thm)],[187]) ).
tff(228,plain,
i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))) = mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),
inference(transitivity,[status(thm)],[194,197,227,200,203]) ).
tff(229,plain,
mult(i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),i(mult(c,op_k(a,b)))) = mult(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),mult(i(c),i(op_k(a,b)))),
inference(monotonicity,[status(thm)],[228,72]) ).
tff(230,plain,
( ~ ! [B: $i,A: $i] : ( i(mult(A,B)) = mult(i(A),i(B)) )
| ( i(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)))) = mult(i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),i(mult(c,op_k(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(231,plain,
i(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)))) = mult(i(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c)))),i(mult(c,op_k(a,b)))),
inference(unit_resolution,[status(thm)],[230,70]) ).
tff(232,plain,
i(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b))))) = i(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)))),
inference(monotonicity,[status(thm)],[224]) ).
tff(233,plain,
i(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b))))) = mult(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),mult(i(c),i(op_k(a,b)))),
inference(transitivity,[status(thm)],[232,231,229]) ).
tff(234,plain,
mult(i(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b))))),mult(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))))) = mult(mult(mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c)),mult(i(c),i(op_k(a,b)))),mult(mult(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(mult(c,op_k(a,b)),op_k(op_k(a,b),c))),asoc(mult(i(mult(c,op_k(a,b))),i(op_k(op_k(a,b),c))),mult(c,op_k(a,b)),op_k(op_k(a,b),c)))),
inference(monotonicity,[status(thm)],[233,226]) ).
tff(235,plain,
( ~ ! [B: $i,A: $i] : ( mult(i(A),mult(A,B)) = B )
| ( mult(i(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b))))),mult(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))))) = mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
mult(i(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b))))),mult(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))))) = mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))),
inference(unit_resolution,[status(thm)],[235,25]) ).
tff(237,plain,
mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))) = mult(i(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b))))),mult(mult(mult(i(op_k(a,b)),mult(i(c),mult(c,op_k(a,b)))),asoc(i(op_k(a,b)),i(c),mult(c,op_k(a,b)))),mult(mult(i(op_k(a,b)),mult(op_k(a,b),op_k(op_k(a,b),c))),asoc(i(op_k(a,b)),op_k(a,b),op_k(op_k(a,b),c))))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
op_k(op_k(a,b),c) = mult(unit,op_k(op_k(a,b),c)),
inference(symmetry,[status(thm)],[212]) ).
tff(239,plain,
op_k(op_k(a,b),c) = unit,
inference(transitivity,[status(thm)],[238,213,216,237,234,208,90,82,80,9]) ).
tff(240,plain,
( ( op_k(op_k(a,b),c) != unit )
<=> ( op_k(op_k(a,b),c) != unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,axiom,
op_k(op_k(a,b),c) != unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(242,plain,
op_k(op_k(a,b),c) != unit,
inference(modus_ponens,[status(thm)],[241,240]) ).
tff(243,plain,
$false,
inference(unit_resolution,[status(thm)],[242,239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP728-1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.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 16:59:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 268.62/268.92 % SZS status Unsatisfiable
% 268.62/268.92 % SZS output start Proof
% See solution above
% 268.62/268.94 % E exiting
%------------------------------------------------------------------------------