%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP679-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:08:27 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 79 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 104 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 14 ~; 10 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 82 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(op_c_type,type,
op_c: $i ).
tff(a_type,type,
a: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(unit_type,type,
unit: $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
tff(5,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(a,mult(op_c,op_c)))) = mult(a,mult(op_c,op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ld(op_c,mult(op_c,mult(a,mult(op_c,op_c)))) = mult(a,mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( mult(op_c,A) = mult(A,op_c) )
<=> ( mult(op_c,A) = mult(A,op_c) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
tff(14,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(op_c,mult(a,op_c))) = mult(mult(op_c,mult(a,op_c)),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
mult(op_c,mult(op_c,mult(a,op_c))) = mult(mult(op_c,mult(a,op_c)),op_c),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
mult(mult(op_c,mult(a,op_c)),op_c) = mult(op_c,mult(op_c,mult(a,op_c))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(a,mult(op_c,op_c))) = mult(mult(op_c,mult(a,op_c)),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
mult(op_c,mult(a,mult(op_c,op_c))) = mult(mult(op_c,mult(a,op_c)),op_c),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
mult(op_c,mult(a,mult(op_c,op_c))) = mult(op_c,mult(op_c,mult(a,op_c))),
inference(transitivity,[status(thm)],[28,19]) ).
tff(30,plain,
ld(op_c,mult(op_c,mult(a,mult(op_c,op_c)))) = ld(op_c,mult(op_c,mult(op_c,mult(a,op_c)))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
ld(op_c,mult(op_c,mult(op_c,mult(a,op_c)))) = ld(op_c,mult(op_c,mult(a,mult(op_c,op_c)))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(op_c,mult(a,op_c)))) = mult(op_c,mult(a,op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
ld(op_c,mult(op_c,mult(op_c,mult(a,op_c)))) = mult(op_c,mult(a,op_c)),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
mult(op_c,mult(a,op_c)) = ld(op_c,mult(op_c,mult(op_c,mult(a,op_c)))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [A: $i] :
refl(( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
tff(39,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,op_c) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
mult(unit,op_c) = op_c,
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
^ [A: $i] :
refl(( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
tff(48,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(op_c,unit) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
mult(op_c,unit) = op_c,
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
mult(unit,mult(op_c,unit)) = mult(unit,op_c),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
mult(unit,mult(op_c,unit)) = op_c,
inference(transitivity,[status(thm)],[53,43]) ).
tff(55,plain,
mult(mult(unit,mult(op_c,unit)),mult(a,op_c)) = mult(op_c,mult(a,op_c)),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(op_c,mult(unit,mult(a,op_c)))) = mult(mult(unit,mult(op_c,unit)),mult(a,op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
mult(unit,mult(op_c,mult(unit,mult(a,op_c)))) = mult(mult(unit,mult(op_c,unit)),mult(a,op_c)),
inference(unit_resolution,[status(thm)],[56,26]) ).
tff(58,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,a) = mult(a,op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
mult(op_c,a) = mult(a,op_c),
inference(unit_resolution,[status(thm)],[58,16]) ).
tff(60,plain,
mult(unit,mult(op_c,a)) = mult(unit,mult(a,op_c)),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
mult(unit,mult(a,op_c)) = mult(unit,mult(op_c,a)),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
mult(op_c,mult(unit,mult(a,op_c))) = mult(op_c,mult(unit,mult(op_c,a))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
mult(op_c,mult(unit,mult(op_c,a))) = mult(op_c,mult(unit,mult(a,op_c))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(unit,mult(op_c,a))) = mult(mult(op_c,mult(unit,op_c)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
mult(op_c,mult(unit,mult(op_c,a))) = mult(mult(op_c,mult(unit,op_c)),a),
inference(unit_resolution,[status(thm)],[64,26]) ).
tff(66,plain,
mult(mult(op_c,mult(unit,op_c)),a) = mult(op_c,mult(unit,mult(op_c,a))),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
mult(op_c,mult(unit,op_c)) = mult(op_c,op_c),
inference(monotonicity,[status(thm)],[43]) ).
tff(68,plain,
mult(mult(op_c,mult(unit,op_c)),a) = mult(mult(op_c,op_c),a),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
mult(mult(op_c,op_c),a) = mult(mult(op_c,mult(unit,op_c)),a),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
mult(mult(op_c,op_c),a) = mult(op_c,mult(unit,mult(a,op_c))),
inference(transitivity,[status(thm)],[69,66,63]) ).
tff(71,plain,
mult(unit,mult(mult(op_c,op_c),a)) = mult(unit,mult(op_c,mult(unit,mult(a,op_c)))),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(mult(op_c,op_c),a)) = mult(mult(op_c,op_c),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
mult(unit,mult(mult(op_c,op_c),a)) = mult(mult(op_c,op_c),a),
inference(unit_resolution,[status(thm)],[72,41]) ).
tff(74,plain,
mult(mult(op_c,op_c),a) = mult(unit,mult(mult(op_c,op_c),a)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
mult(mult(op_c,op_c),a) = mult(a,mult(op_c,op_c)),
inference(transitivity,[status(thm)],[74,71,57,55,34,31,9]) ).
tff(76,plain,
( ( mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)) )
<=> ( mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(78,plain,
mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP679-1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 16:53:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------