%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP001-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:06:47 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.38s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 38
% Syntax : Number of formulae : 126 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 161 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 56 ( 20 ~; 16 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 6 ( 6 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; 4 con; 0-2 aty)
% Number of variables : 104 ( 96 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_type,type,
c: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
( ( multiply(a,b) = c )
<=> ( multiply(a,b) = c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
tff(3,plain,
multiply(a,b) = c,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c = multiply(a,b),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
multiply(c,inverse(b)) = multiply(multiply(a,b),inverse(b)),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
multiply(multiply(a,b),inverse(b)) = multiply(c,inverse(b)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
tff(11,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),inverse(b)) = multiply(a,multiply(b,inverse(b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
multiply(multiply(a,b),inverse(b)) = multiply(a,multiply(b,inverse(b))),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
multiply(a,multiply(b,inverse(b))) = multiply(multiply(a,b),inverse(b)),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
refl(( ( multiply(X,inverse(X)) = identity )
<=> ( multiply(X,inverse(X)) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
tff(21,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(b,inverse(b)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
multiply(b,inverse(b)) = identity,
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
multiply(a,multiply(b,inverse(b))) = multiply(a,identity),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
multiply(a,identity) = multiply(a,multiply(b,inverse(b))),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
^ [X: $i] :
refl(( ( multiply(X,identity) = X )
<=> ( multiply(X,identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [X: $i] : ( multiply(X,identity) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
tff(32,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(a,identity) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
multiply(a,identity) = a,
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
a = multiply(a,identity),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
a = multiply(c,inverse(b)),
inference(transitivity,[status(thm)],[37,27,16,6]) ).
tff(39,plain,
multiply(a,b) = multiply(multiply(c,inverse(b)),b),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
multiply(multiply(c,inverse(b)),b) = multiply(a,b),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,inverse(b)),b) = multiply(c,multiply(inverse(b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
multiply(multiply(c,inverse(b)),b) = multiply(c,multiply(inverse(b),b)),
inference(unit_resolution,[status(thm)],[41,13]) ).
tff(43,plain,
multiply(c,multiply(inverse(b),b)) = multiply(multiply(c,inverse(b)),b),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,inverse(b)),a) = multiply(b,multiply(inverse(b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
multiply(multiply(b,inverse(b)),a) = multiply(b,multiply(inverse(b),a)),
inference(unit_resolution,[status(thm)],[44,13]) ).
tff(46,plain,
multiply(multiply(b,inverse(b)),a) = multiply(identity,a),
inference(monotonicity,[status(thm)],[25]) ).
tff(47,plain,
multiply(identity,a) = multiply(multiply(b,inverse(b)),a),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(52,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
a = multiply(identity,a),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
a = multiply(b,multiply(inverse(b),a)),
inference(transitivity,[status(thm)],[57,47,45]) ).
tff(59,plain,
multiply(inverse(b),a) = multiply(inverse(b),multiply(b,multiply(inverse(b),a))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
multiply(inverse(b),multiply(b,multiply(inverse(b),a))) = multiply(inverse(b),a),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
multiply(c,multiply(inverse(b),multiply(b,multiply(inverse(b),a)))) = multiply(c,multiply(inverse(b),a)),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
multiply(c,multiply(inverse(b),a)) = multiply(c,multiply(inverse(b),multiply(b,multiply(inverse(b),a)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
multiply(c,multiply(inverse(b),a)) = multiply(multiply(a,b),multiply(inverse(b),a)),
inference(monotonicity,[status(thm)],[4]) ).
tff(64,plain,
multiply(multiply(a,b),multiply(inverse(b),a)) = multiply(c,multiply(inverse(b),a)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(a,b),multiply(inverse(b),a)) = multiply(a,multiply(b,multiply(inverse(b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
multiply(multiply(a,b),multiply(inverse(b),a)) = multiply(a,multiply(b,multiply(inverse(b),a))),
inference(unit_resolution,[status(thm)],[65,13]) ).
tff(67,plain,
multiply(a,multiply(b,multiply(inverse(b),a))) = multiply(multiply(a,b),multiply(inverse(b),a)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
multiply(b,multiply(inverse(b),a)) = multiply(multiply(b,inverse(b)),a),
inference(symmetry,[status(thm)],[45]) ).
tff(69,plain,
multiply(b,multiply(inverse(b),a)) = a,
inference(transitivity,[status(thm)],[68,46,56]) ).
tff(70,plain,
multiply(a,multiply(b,multiply(inverse(b),a))) = multiply(a,a),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
multiply(a,a) = multiply(a,multiply(b,multiply(inverse(b),a))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
^ [X: $i] :
refl(( ( multiply(X,X) = identity )
<=> ( multiply(X,X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [X: $i] : ( multiply(X,X) = identity )
<=> ! [X: $i] : ( multiply(X,X) = identity ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [X: $i] : ( multiply(X,X) = identity )
<=> ! [X: $i] : ( multiply(X,X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
! [X: $i] : ( multiply(X,X) = identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',squareness) ).
tff(76,plain,
! [X: $i] : ( multiply(X,X) = identity ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [X: $i] : ( multiply(X,X) = identity ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [X: $i] : ( multiply(X,X) = identity ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [X: $i] : ( multiply(X,X) = identity )
| ( multiply(a,a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
multiply(a,a) = identity,
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
identity = multiply(a,a),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(86,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(b),b) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
multiply(inverse(b),b) = identity,
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
multiply(inverse(b),b) = multiply(c,multiply(inverse(b),multiply(b,multiply(inverse(b),a)))),
inference(transitivity,[status(thm)],[90,81,71,67,64,62]) ).
tff(92,plain,
multiply(c,multiply(inverse(b),b)) = multiply(c,multiply(c,multiply(inverse(b),multiply(b,multiply(inverse(b),a))))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
multiply(c,multiply(c,multiply(inverse(b),multiply(b,multiply(inverse(b),a))))) = multiply(c,multiply(inverse(b),b)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(c,c),multiply(inverse(b),multiply(b,multiply(inverse(b),a)))) = multiply(c,multiply(c,multiply(inverse(b),multiply(b,multiply(inverse(b),a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
multiply(multiply(c,c),multiply(inverse(b),multiply(b,multiply(inverse(b),a)))) = multiply(c,multiply(c,multiply(inverse(b),multiply(b,multiply(inverse(b),a))))),
inference(unit_resolution,[status(thm)],[94,13]) ).
tff(96,plain,
multiply(b,a) = multiply(b,multiply(a,identity)),
inference(monotonicity,[status(thm)],[37]) ).
tff(97,plain,
multiply(b,multiply(b,multiply(inverse(b),a))) = multiply(b,a),
inference(monotonicity,[status(thm)],[69]) ).
tff(98,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(b,b),multiply(inverse(b),a)) = multiply(b,multiply(b,multiply(inverse(b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
multiply(multiply(b,b),multiply(inverse(b),a)) = multiply(b,multiply(b,multiply(inverse(b),a))),
inference(unit_resolution,[status(thm)],[98,13]) ).
tff(100,plain,
( ~ ! [X: $i] : ( multiply(X,X) = identity )
| ( multiply(b,b) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
multiply(b,b) = identity,
inference(unit_resolution,[status(thm)],[100,78]) ).
tff(102,plain,
identity = multiply(b,b),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
multiply(inverse(b),b) = multiply(b,b),
inference(transitivity,[status(thm)],[90,102]) ).
tff(104,plain,
multiply(multiply(inverse(b),b),multiply(inverse(b),a)) = multiply(multiply(b,b),multiply(inverse(b),a)),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(b),b),multiply(inverse(b),a)) = multiply(inverse(b),multiply(b,multiply(inverse(b),a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
multiply(multiply(inverse(b),b),multiply(inverse(b),a)) = multiply(inverse(b),multiply(b,multiply(inverse(b),a))),
inference(unit_resolution,[status(thm)],[105,13]) ).
tff(107,plain,
multiply(inverse(b),multiply(b,multiply(inverse(b),a))) = multiply(multiply(inverse(b),b),multiply(inverse(b),a)),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
multiply(inverse(b),multiply(b,multiply(inverse(b),a))) = multiply(b,multiply(a,identity)),
inference(transitivity,[status(thm)],[107,104,99,97,96]) ).
tff(109,plain,
( ~ ! [X: $i] : ( multiply(X,X) = identity )
| ( multiply(c,c) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
multiply(c,c) = identity,
inference(unit_resolution,[status(thm)],[109,78]) ).
tff(111,plain,
multiply(multiply(c,c),multiply(inverse(b),multiply(b,multiply(inverse(b),a)))) = multiply(identity,multiply(b,multiply(a,identity))),
inference(monotonicity,[status(thm)],[110,108]) ).
tff(112,plain,
multiply(identity,multiply(b,multiply(a,identity))) = multiply(multiply(c,c),multiply(inverse(b),multiply(b,multiply(inverse(b),a)))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
multiply(b,multiply(a,identity)) = multiply(b,a),
inference(symmetry,[status(thm)],[96]) ).
tff(114,plain,
multiply(identity,multiply(b,multiply(a,identity))) = multiply(identity,multiply(b,a)),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
multiply(identity,multiply(b,a)) = multiply(identity,multiply(b,multiply(a,identity))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(identity,b),a) = multiply(identity,multiply(b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
multiply(multiply(identity,b),a) = multiply(identity,multiply(b,a)),
inference(unit_resolution,[status(thm)],[116,13]) ).
tff(118,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
multiply(identity,b) = b,
inference(unit_resolution,[status(thm)],[118,54]) ).
tff(120,plain,
multiply(multiply(identity,b),a) = multiply(b,a),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
multiply(b,a) = multiply(multiply(identity,b),a),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
multiply(b,a) = c,
inference(transitivity,[status(thm)],[121,117,115,112,95,93,43,40,3]) ).
tff(123,plain,
( ( multiply(b,a) != c )
<=> ( multiply(b,a) != c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,axiom,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
tff(125,plain,
multiply(b,a) != c,
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
$false,
inference(unit_resolution,[status(thm)],[125,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP001-2 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 15:29:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.17/0.38 % SZS status Unsatisfiable
% 0.17/0.38 % SZS output start Proof
% See solution above
% 0.17/0.39 % E exiting
%------------------------------------------------------------------------------