TSTP Solution File: ANA133-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA133-1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 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 : Wed Aug 30 17:14:20 EDT 2023
% Result : Unsatisfiable 1.53s 1.59s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 45 ( 36 unt; 9 typ; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
'+': ( $i * $i ) > $i ).
tff(decl_23,type,
times: ( $i * $i ) > $i ).
tff(decl_24,type,
zero: $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
minus: $i > $i ).
tff(decl_27,type,
d: $i > $i ).
tff(decl_28,type,
x: $i ).
tff(decl_29,type,
sin: $i > $i ).
tff(decl_30,type,
cos: $i > $i ).
cnf(derivative_of_times,axiom,
d(times(X1,X2)) = '+'(times(X1,d(X2)),times(X2,d(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_times) ).
cnf(commutativity_of_times,axiom,
times(X1,X2) = times(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_times) ).
cnf(associtivity_of_plus,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associtivity_of_plus) ).
cnf(minus,axiom,
'+'(X1,minus(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus) ).
cnf(plus_zero,axiom,
'+'(zero,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
cnf(derivative_of_x,axiom,
d(x) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_x) ).
cnf(times_one,axiom,
times(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_one) ).
cnf(commutativity_of_plus,axiom,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_plus) ).
cnf(derivative_of_cos,axiom,
d(cos(X1)) = minus(times(sin(X1),d(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_cos) ).
cnf(derivative_of_sin,axiom,
d(sin(X1)) = times(cos(X1),d(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_sin) ).
cnf(derivative_of_plus,axiom,
d('+'(X1,X2)) = '+'(d(X1),d(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_plus) ).
cnf(goal,negated_conjecture,
d(X1) != times(x,cos(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c_0_12,axiom,
d(times(X1,X2)) = '+'(times(X1,d(X2)),times(X2,d(X1))),
derivative_of_times ).
cnf(c_0_13,axiom,
times(X1,X2) = times(X2,X1),
commutativity_of_times ).
cnf(c_0_14,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
associtivity_of_plus ).
cnf(c_0_15,axiom,
'+'(X1,minus(X1)) = zero,
minus ).
cnf(c_0_16,axiom,
'+'(zero,X1) = X1,
plus_zero ).
cnf(c_0_17,plain,
'+'(times(X1,d(X2)),times(d(X1),X2)) = d(times(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,axiom,
d(x) = one,
derivative_of_x ).
cnf(c_0_19,axiom,
times(one,X1) = X1,
times_one ).
cnf(c_0_20,axiom,
'+'(X1,X2) = '+'(X2,X1),
commutativity_of_plus ).
cnf(c_0_21,plain,
'+'(X1,'+'(minus(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_22,plain,
'+'(X1,times(x,d(X1))) = d(times(x,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_23,plain,
'+'(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_24,axiom,
d(cos(X1)) = minus(times(sin(X1),d(X1))),
derivative_of_cos ).
cnf(c_0_25,axiom,
d(sin(X1)) = times(cos(X1),d(X1)),
derivative_of_sin ).
cnf(c_0_26,plain,
'+'(X1,d(times(x,minus(X1)))) = times(x,d(minus(X1))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
minus(minus(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15]),c_0_23]) ).
cnf(c_0_28,plain,
minus(times(d(X1),sin(X1))) = d(cos(X1)),
inference(rw,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_29,plain,
times(d(X1),cos(X1)) = d(sin(X1)),
inference(rw,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_30,plain,
'+'(d(times(x,X1)),minus(X1)) = times(x,d(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_20]) ).
cnf(c_0_31,plain,
minus(sin(x)) = d(cos(x)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_19]) ).
cnf(c_0_32,axiom,
d('+'(X1,X2)) = '+'(d(X1),d(X2)),
derivative_of_plus ).
cnf(c_0_33,plain,
d(sin(x)) = cos(x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_18]),c_0_19]) ).
cnf(c_0_34,negated_conjecture,
d(X1) != times(x,cos(x)),
goal ).
cnf(c_0_35,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA133-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:40:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 1.53/1.59 % Version : CSE_E---1.5
% 1.53/1.59 % Problem : theBenchmark.p
% 1.53/1.59 % Proof found
% 1.53/1.59 % SZS status Theorem for theBenchmark.p
% 1.53/1.59 % SZS output start Proof
% See solution above
% 1.53/1.60 % Total time : 1.006000 s
% 1.53/1.60 % SZS output end Proof
% 1.53/1.60 % Total time : 1.009000 s
%------------------------------------------------------------------------------