%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA133-1 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 : Tue May 5 04:09:29 PM UTC 2026
% Result : Unsatisfiable 8.66s 5.91s
% Output : CNFRefutation 8.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 9 RR)
% Number of literals : 37 ( 36 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% 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 : 49 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(derivative_of_cos,axiom,
d(cos(X1)) = minus(times(sin(X1),d(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_cos) ).
cnf(commutativity_of_times,axiom,
times(X1,X2) = times(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_times) ).
cnf(derivative_of_x,axiom,
d(x) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_x) ).
cnf(times_one,axiom,
times(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
cnf(associtivity_of_plus,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associtivity_of_plus) ).
cnf(derivative_of_times,axiom,
d(times(X1,X2)) = '+'(times(X1,d(X2)),times(X2,d(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_times) ).
cnf(commutativity_of_plus,axiom,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_plus) ).
cnf(minus,axiom,
'+'(X1,minus(X1)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus) ).
cnf(plus_zero,axiom,
'+'(zero,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
cnf(derivative_of_sin,axiom,
d(sin(X1)) = times(cos(X1),d(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_sin) ).
cnf(goal,negated_conjecture,
d(X1) != times(x,cos(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(derivative_of_plus,axiom,
d('+'(X1,X2)) = '+'(d(X1),d(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_plus) ).
cnf(c_0_12,axiom,
d(cos(X1)) = minus(times(sin(X1),d(X1))),
derivative_of_cos ).
cnf(c_0_13,axiom,
times(X1,X2) = times(X2,X1),
commutativity_of_times ).
cnf(c_0_14,plain,
minus(times(d(X1),sin(X1))) = d(cos(X1)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
d(x) = one,
derivative_of_x ).
cnf(c_0_16,axiom,
times(one,X1) = X1,
times_one ).
cnf(c_0_17,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
associtivity_of_plus ).
cnf(c_0_18,axiom,
d(times(X1,X2)) = '+'(times(X1,d(X2)),times(X2,d(X1))),
derivative_of_times ).
cnf(c_0_19,axiom,
'+'(X1,X2) = '+'(X2,X1),
commutativity_of_plus ).
cnf(c_0_20,axiom,
'+'(X1,minus(X1)) = zero,
minus ).
cnf(c_0_21,plain,
minus(sin(x)) = d(cos(x)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_22,axiom,
'+'(zero,X1) = X1,
plus_zero ).
cnf(c_0_23,axiom,
d(sin(X1)) = times(cos(X1),d(X1)),
derivative_of_sin ).
cnf(c_0_24,plain,
'+'(times(X1,d(X2)),'+'(times(X2,d(X1)),X3)) = '+'(d(times(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
times(X1,one) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_26,plain,
'+'(X1,'+'(X2,X3)) = '+'(X2,'+'(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_17]) ).
cnf(c_0_27,plain,
'+'(sin(x),d(cos(x))) = zero,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
'+'(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_29,plain,
times(d(X1),cos(X1)) = d(sin(X1)),
inference(rw,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_30,negated_conjecture,
d(X1) != times(x,cos(x)),
goal ).
cnf(c_0_31,axiom,
d('+'(X1,X2)) = '+'(d(X1),d(X2)),
derivative_of_plus ).
cnf(c_0_32,plain,
'+'(X1,'+'(times(x,d(X1)),X2)) = '+'(d(times(x,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_15]),c_0_25]),c_0_26]) ).
cnf(c_0_33,plain,
'+'(sin(x),'+'(X1,d(cos(x)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_34,plain,
d(sin(x)) = cos(x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_15]),c_0_16]) ).
cnf(c_0_35,negated_conjecture,
'+'(d(X1),d(X2)) != times(x,cos(x)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA133-1 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:38:20 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 8.66/5.91 % Version : CSE_E---1.7
% 8.66/5.91 % Problem : theBenchmark.p
% 8.66/5.91 % SZS status Unsatisfiable for theBenchmark.p
% 8.66/5.91 % SZS output start CNFRefutation
% See solution above
% 8.66/5.94 % Total time : 4.369s
%------------------------------------------------------------------------------