%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP534-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:02 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 25
% Syntax : Number of formulae : 79 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 102 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 15 ~; 11 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 100 !; 0 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b2_type,type,
b2: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( divide(divide(A,divide(divide(A,B),C)),B) = C )
<=> ( divide(divide(A,divide(divide(A,B),C)),B) = C ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C )
<=> ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C )
| ( divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)),a2)),divide(divide(inverse(b2),inverse(b2)),a2)) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)),a2)),divide(divide(inverse(b2),inverse(b2)),a2)) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(inverse(b2),inverse(b2)),a2),a2) = divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)),a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(divide(divide(inverse(b2),inverse(b2)),a2),a2) = divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)),a2)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(divide(inverse(b2),inverse(b2)),a2),a2) = divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
multiply(divide(divide(inverse(b2),inverse(b2)),a2),a2) = divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,plain,
divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)) = multiply(divide(divide(inverse(b2),inverse(b2)),a2),a2),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C )
| ( divide(divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)),multiply(inverse(b2),b2)) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
divide(divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)),multiply(inverse(b2),b2)) = a2,
inference(unit_resolution,[status(thm)],[22,7]) ).
tff(24,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(inverse(b2),b2) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
multiply(inverse(b2),b2) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)),
inference(unit_resolution,[status(thm)],[24,16]) ).
tff(26,plain,
divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)) = multiply(inverse(b2),b2),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
^ [B: $i,A: $i] :
refl(( ( inverse(A) = divide(divide(B,B),A) )
<=> ( inverse(A) = divide(divide(B,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
<=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
<=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
tff(31,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
| ( inverse(b2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
inverse(b2) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2) = inverse(b2),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)) = divide(inverse(b2),inverse(b2)),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
divide(inverse(b2),inverse(b2)) = divide(inverse(b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),b2)),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
divide(inverse(b2),inverse(b2)) = multiply(inverse(b2),b2),
inference(transitivity,[status(thm)],[38,26]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
multiply(multiply(inverse(b2),b2),a2) = divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)),
inference(unit_resolution,[status(thm)],[40,16]) ).
tff(42,plain,
multiply(inverse(b2),b2) = divide(inverse(b2),inverse(b2)),
inference(transitivity,[status(thm)],[25,37]) ).
tff(43,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(divide(inverse(b2),inverse(b2)),a2),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) = multiply(multiply(inverse(b2),b2),a2),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
| ( multiply(divide(inverse(b2),inverse(b2)),a2) = divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) = divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),
inference(unit_resolution,[status(thm)],[45,16]) ).
tff(47,plain,
divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)) = multiply(divide(inverse(b2),inverse(b2)),a2),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)) = divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)),
inference(transitivity,[status(thm)],[47,44,41]) ).
tff(49,plain,
divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2))) = divide(divide(multiply(inverse(b2),b2),divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),a2)),multiply(inverse(b2),b2)),
inference(monotonicity,[status(thm)],[48,39]) ).
tff(50,plain,
divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2))) = a2,
inference(transitivity,[status(thm)],[49,23]) ).
tff(51,plain,
divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2)))) = divide(divide(inverse(b2),inverse(b2)),a2),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
divide(divide(inverse(b2),inverse(b2)),a2) = divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2)))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)) = divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),a2)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),a2)) = divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( divide(divide(A,divide(divide(A,B),C)),B) = C )
| ( divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),a2)) = divide(inverse(b2),inverse(b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),a2)) = divide(inverse(b2),inverse(b2)),
inference(unit_resolution,[status(thm)],[55,7]) ).
tff(57,plain,
divide(inverse(b2),inverse(b2)) = divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)),divide(inverse(b2),inverse(b2)))),divide(divide(inverse(b2),inverse(b2)),a2)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
^ [A: $i] :
refl(( ( identity = divide(A,A) )
<=> ( identity = divide(A,A) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [A: $i] : ( identity = divide(A,A) )
<=> ! [A: $i] : ( identity = divide(A,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [A: $i] : ( identity = divide(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
tff(62,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [A: $i] : ( identity = divide(A,A) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(inverse(b2),inverse(b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
identity = divide(inverse(b2),inverse(b2)),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ ! [A: $i] : ( identity = divide(A,A) )
| ( identity = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
identity = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(unit_resolution,[status(thm)],[67,64]) ).
tff(69,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = identity,
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)) = divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)),a2)),
inference(transitivity,[status(thm)],[69,66,57,54,21,18]) ).
tff(71,plain,
divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(inverse(b2),inverse(b2)),a2)) = divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(divide(divide(inverse(b2),inverse(b2)),a2),divide(divide(inverse(b2),inverse(b2)),a2)),a2)),divide(divide(inverse(b2),inverse(b2)),a2)),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
divide(inverse(b2),inverse(b2)) = identity,
inference(symmetry,[status(thm)],[66]) ).
tff(73,plain,
divide(inverse(b2),inverse(b2)) = divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),
inference(transitivity,[status(thm)],[72,68]) ).
tff(74,plain,
divide(divide(inverse(b2),inverse(b2)),divide(divide(inverse(b2),inverse(b2)),a2)) = divide(divide(multiply(inverse(b2),b2),multiply(inverse(b2),b2)),divide(divide(inverse(b2),inverse(b2)),a2)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[43,46,74,71,9]) ).
tff(76,plain,
( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
<=> ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
tff(78,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP534-1 : TPTP v9.0.0. Released v2.6.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:16:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
% 0.21/0.41 % E exiting
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