%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:51:19 AM UTC 2026
% Result : Unsatisfiable 30.89s 4.25s
% Output : CNFRefutation 30.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 109 ( 109 unt; 0 def)
% Number of atoms : 109 ( 108 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 138 ( 16 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_plus,axiom,
! [VAR_0,VAR_1] : '+'(VAR_0,VAR_1) = '+'(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_plus) ).
cnf(c_1,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[commutativity_of_plus]) ).
fof(associtivity_of_plus,axiom,
! [VAR_0,VAR_1,VAR_2] : '+'(VAR_0,'+'(VAR_1,VAR_2)) = '+'('+'(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associtivity_of_plus) ).
cnf(c_2,plain,
'+'(A,'+'(B,C)) = '+'('+'(A,B),C),
inference(clausify,[status(thm)],[associtivity_of_plus]) ).
cnf(c_3,plain,
'+'('+'(A,B),C) = '+'(A,'+'(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(commutativity_of_times,axiom,
! [VAR_0,VAR_1] : times(VAR_0,VAR_1) = times(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_times) ).
cnf(c_4,plain,
times(A,B) = times(B,A),
inference(clausify,[status(thm)],[commutativity_of_times]) ).
fof(associativity_of_times,axiom,
! [VAR_0,VAR_1,VAR_2] : times(VAR_0,times(VAR_1,VAR_2)) = times(times(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_times) ).
cnf(c_5,plain,
times(A,times(B,C)) = times(times(A,B),C),
inference(clausify,[status(thm)],[associativity_of_times]) ).
cnf(c_6,plain,
times(times(A,B),C) = times(A,times(B,C)),
inference(copy,[status(thm)],[c_5]) ).
fof(plus_zero,axiom,
! [VAR_0] : '+'(zero,VAR_0) = VAR_0,
file('theBenchmark.p',plus_zero) ).
cnf(c_7,plain,
'+'(zero,A) = A,
inference(clausify,[status(thm)],[plus_zero]) ).
fof(times_zero,axiom,
! [VAR_0] : times(zero,VAR_0) = zero,
file('theBenchmark.p',times_zero) ).
cnf(c_8,plain,
times(zero,A) = zero,
inference(clausify,[status(thm)],[times_zero]) ).
fof(times_one,axiom,
! [VAR_0] : times(one,VAR_0) = VAR_0,
file('theBenchmark.p',times_one) ).
cnf(c_9,plain,
times(one,A) = A,
inference(clausify,[status(thm)],[times_one]) ).
fof(distributivity,axiom,
! [VAR_0,VAR_1,VAR_2] : times(VAR_0,'+'(VAR_1,VAR_2)) = '+'(times(VAR_0,VAR_1),times(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity) ).
cnf(c_10,plain,
times(A,'+'(B,C)) = '+'(times(A,B),times(A,C)),
inference(clausify,[status(thm)],[distributivity]) ).
fof(minus,axiom,
! [VAR_0] : '+'(VAR_0,minus(VAR_0)) = zero,
file('theBenchmark.p',minus) ).
cnf(c_11,plain,
'+'(A,minus(A)) = zero,
inference(clausify,[status(thm)],[minus]) ).
fof(derivative_of_zero,axiom,
d(zero) = zero,
file('theBenchmark.p',derivative_of_zero) ).
cnf(c_12,plain,
d(zero) = zero,
inference(clausify,[status(thm)],[derivative_of_zero]) ).
fof(derivative_of_one,axiom,
d(one) = zero,
file('theBenchmark.p',derivative_of_one) ).
cnf(c_13,plain,
d(one) = zero,
inference(clausify,[status(thm)],[derivative_of_one]) ).
fof(derivative_of_x,axiom,
d(x) = one,
file('theBenchmark.p',derivative_of_x) ).
cnf(c_14,plain,
d(x) = one,
inference(clausify,[status(thm)],[derivative_of_x]) ).
fof(derivative_of_plus,axiom,
! [VAR_0,VAR_1] : d('+'(VAR_0,VAR_1)) = '+'(d(VAR_0),d(VAR_1)),
file('theBenchmark.p',derivative_of_plus) ).
cnf(c_15,plain,
d('+'(A,B)) = '+'(d(A),d(B)),
inference(clausify,[status(thm)],[derivative_of_plus]) ).
fof(derivative_of_times,axiom,
! [VAR_0,VAR_1] : d(times(VAR_0,VAR_1)) = '+'(times(VAR_0,d(VAR_1)),times(VAR_1,d(VAR_0))),
file('theBenchmark.p',derivative_of_times) ).
cnf(c_16,plain,
d(times(A,B)) = '+'(times(A,d(B)),times(B,d(A))),
inference(clausify,[status(thm)],[derivative_of_times]) ).
fof(derivative_of_sin,axiom,
! [VAR_0] : d(sin(VAR_0)) = times(cos(VAR_0),d(VAR_0)),
file('theBenchmark.p',derivative_of_sin) ).
cnf(c_17,plain,
d(sin(A)) = times(cos(A),d(A)),
inference(clausify,[status(thm)],[derivative_of_sin]) ).
cnf(c_18,plain,
d(sin(A)) = times(d(A),cos(A)),
inference(paramod,[status(thm)],[c_4,c_17]) ).
fof(derivative_of_cos,axiom,
! [VAR_0] : d(cos(VAR_0)) = minus(times(sin(VAR_0),d(VAR_0))),
file('theBenchmark.p',derivative_of_cos) ).
cnf(c_19,plain,
d(cos(A)) = minus(times(sin(A),d(A))),
inference(clausify,[status(thm)],[derivative_of_cos]) ).
cnf(c_4956,plain,
d(cos(A)) = minus(times(d(A),sin(A))),
inference(paramod,[status(thm)],[c_4,c_19]) ).
cnf(c_20,plain,
minus(times(d(A),sin(A))) = d(cos(A)),
inference(copy,[status(thm)],[c_4956]) ).
fof(goal,axiom,
! [VAR_0] : d(VAR_0) != times(x,cos(x)),
file('theBenchmark.p',goal) ).
cnf(c_21,plain,
d(A) != times(x,cos(x)),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_4957,plain,
'+'('+'(A,B),C) = '+'(B,'+'(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_23,plain,
'+'(A,'+'(B,C)) = '+'(B,'+'(A,C)),
inference(paramod,[status(thm)],[c_3,c_4957]) ).
cnf(c_4958,plain,
A = '+'(A,zero),
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_26,plain,
'+'(A,zero) = A,
inference(copy,[status(thm)],[c_4958]) ).
cnf(c_4959,plain,
zero = times(A,zero),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_27,plain,
times(A,zero) = zero,
inference(copy,[status(thm)],[c_4959]) ).
cnf(c_4960,plain,
A = times(A,one),
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_28,plain,
times(A,one) = A,
inference(copy,[status(thm)],[c_4960]) ).
cnf(c_4961,plain,
'+'(zero,A) = '+'(B,'+'(minus(B),A)),
inference(paramod,[status(thm)],[c_11,c_3]) ).
cnf(c_4962,plain,
A = '+'(B,'+'(minus(B),A)),
inference(paramod,[status(thm)],[c_7,c_4961]) ).
cnf(c_31,plain,
'+'(A,'+'(minus(A),B)) = B,
inference(copy,[status(thm)],[c_4962]) ).
cnf(c_4963,plain,
times(A,zero) = '+'(times(A,B),times(A,minus(B))),
inference(paramod,[status(thm)],[c_11,c_10]) ).
cnf(c_4964,plain,
zero = '+'(times(A,B),times(A,minus(B))),
inference(paramod,[status(thm)],[c_27,c_4963]) ).
cnf(c_34,plain,
'+'(times(A,B),times(A,minus(B))) = zero,
inference(copy,[status(thm)],[c_4964]) ).
cnf(c_4965,plain,
d(zero) = '+'(d(A),d(minus(A))),
inference(paramod,[status(thm)],[c_11,c_15]) ).
cnf(c_4966,plain,
zero = '+'(d(A),d(minus(A))),
inference(paramod,[status(thm)],[c_12,c_4965]) ).
cnf(c_35,plain,
'+'(d(A),d(minus(A))) = zero,
inference(copy,[status(thm)],[c_4966]) ).
cnf(c_4967,plain,
minus(times(one,sin(x))) = d(cos(x)),
inference(paramod,[status(thm)],[c_14,c_20]) ).
cnf(c_39,plain,
minus(sin(x)) = d(cos(x)),
inference(paramod,[status(thm)],[c_9,c_4967]) ).
cnf(c_4968,plain,
'+'(d(A),d(B)) != times(x,cos(x)),
inference(paramod,[status(thm)],[c_15,c_21]) ).
cnf(c_43,plain,
times(x,cos(x)) != '+'(d(A),d(B)),
inference(copy,[status(thm)],[c_4968]) ).
cnf(c_4969,plain,
'+'(A,zero) = '+'(B,'+'(A,minus(B))),
inference(paramod,[status(thm)],[c_11,c_23]) ).
cnf(c_4970,plain,
A = '+'(B,'+'(A,minus(B))),
inference(paramod,[status(thm)],[c_26,c_4969]) ).
cnf(c_46,plain,
'+'(A,'+'(B,minus(A))) = B,
inference(copy,[status(thm)],[c_4970]) ).
cnf(c_4971,plain,
times(x,cos(x)) != '+'('+'(times(A,d(B)),times(B,d(A))),d(C)),
inference(paramod,[status(thm)],[c_16,c_43]) ).
cnf(c_49,plain,
times(x,cos(x)) != '+'(times(A,d(B)),'+'(times(B,d(A)),d(C))),
inference(paramod,[status(thm)],[c_3,c_4971]) ).
cnf(c_4972,plain,
'+'(zero,d(minus(one))) = zero,
inference(paramod,[status(thm)],[c_13,c_35]) ).
cnf(c_82,plain,
d(minus(one)) = zero,
inference(paramod,[status(thm)],[c_7,c_4972]) ).
cnf(c_4973,plain,
'+'(A,zero) = minus(minus(A)),
inference(paramod,[status(thm)],[c_11,c_31]) ).
cnf(c_4974,plain,
A = minus(minus(A)),
inference(paramod,[status(thm)],[c_26,c_4973]) ).
cnf(c_97,plain,
minus(minus(A)) = A,
inference(copy,[status(thm)],[c_4974]) ).
cnf(c_4975,plain,
minus(d(cos(x))) = sin(x),
inference(paramod,[status(thm)],[c_39,c_97]) ).
cnf(c_118,plain,
sin(x) = minus(d(cos(x))),
inference(copy,[status(thm)],[c_4975]) ).
cnf(c_4976,plain,
d(minus(d(cos(x)))) = times(d(x),cos(x)),
inference(paramod,[status(thm)],[c_118,c_18]) ).
cnf(c_4977,plain,
d(minus(d(cos(x)))) = times(one,cos(x)),
inference(paramod,[status(thm)],[c_14,c_4976]) ).
cnf(c_124,plain,
d(minus(d(cos(x)))) = cos(x),
inference(paramod,[status(thm)],[c_9,c_4977]) ).
cnf(c_131,plain,
'+'(A,times(A,minus(one))) = zero,
inference(paramod,[status(thm)],[c_28,c_34]) ).
cnf(c_4978,plain,
'+'(A,zero) = times(minus(A),minus(one)),
inference(paramod,[status(thm)],[c_131,c_31]) ).
cnf(c_4979,plain,
A = times(minus(A),minus(one)),
inference(paramod,[status(thm)],[c_26,c_4978]) ).
cnf(c_159,plain,
times(minus(A),minus(one)) = A,
inference(copy,[status(thm)],[c_4979]) ).
cnf(c_4980,plain,
A = times(minus(one),minus(A)),
inference(paramod,[status(thm)],[c_159,c_4]) ).
cnf(c_160,plain,
times(minus(one),minus(A)) = A,
inference(copy,[status(thm)],[c_4980]) ).
cnf(c_168,plain,
times(A,minus(one)) = minus(A),
inference(paramod,[status(thm)],[c_97,c_159]) ).
cnf(c_186,plain,
'+'(minus(A),'+'(B,A)) = B,
inference(paramod,[status(thm)],[c_97,c_46]) ).
cnf(c_201,plain,
times(minus(one),A) = minus(A),
inference(paramod,[status(thm)],[c_97,c_160]) ).
cnf(c_4981,plain,
times(minus(A),B) = times(A,times(minus(one),B)),
inference(paramod,[status(thm)],[c_168,c_6]) ).
cnf(c_210,plain,
times(minus(A),B) = times(A,minus(B)),
inference(paramod,[status(thm)],[c_201,c_4981]) ).
cnf(c_4982,plain,
minus(times(A,B)) = times(A,times(B,minus(one))),
inference(paramod,[status(thm)],[c_168,c_6]) ).
cnf(c_4983,plain,
minus(times(A,B)) = times(A,minus(B)),
inference(paramod,[status(thm)],[c_168,c_4982]) ).
cnf(c_211,plain,
times(A,minus(B)) = minus(times(A,B)),
inference(copy,[status(thm)],[c_4983]) ).
cnf(c_4984,plain,
d(minus(A)) = '+'(times(A,d(minus(one))),times(minus(one),d(A))),
inference(paramod,[status(thm)],[c_168,c_16]) ).
cnf(c_4985,plain,
d(minus(A)) = '+'(times(A,zero),times(minus(one),d(A))),
inference(paramod,[status(thm)],[c_82,c_4984]) ).
cnf(c_4986,plain,
d(minus(A)) = '+'(zero,times(minus(one),d(A))),
inference(paramod,[status(thm)],[c_27,c_4985]) ).
cnf(c_4987,plain,
d(minus(A)) = '+'(zero,times(one,minus(d(A)))),
inference(paramod,[status(thm)],[c_210,c_4986]) ).
cnf(c_4988,plain,
d(minus(A)) = '+'(zero,minus(times(one,d(A)))),
inference(paramod,[status(thm)],[c_211,c_4987]) ).
cnf(c_4989,plain,
d(minus(A)) = '+'(zero,minus(d(A))),
inference(paramod,[status(thm)],[c_9,c_4988]) ).
cnf(c_212,plain,
d(minus(A)) = minus(d(A)),
inference(paramod,[status(thm)],[c_7,c_4989]) ).
cnf(c_225,plain,
minus(d(d(cos(x)))) = cos(x),
inference(paramod,[status(thm)],[c_212,c_124]) ).
cnf(c_4990,plain,
times(x,cos(x)) != '+'(times(A,one),'+'(times(x,d(A)),d(B))),
inference(paramod,[status(thm)],[c_14,c_49]) ).
cnf(c_253,plain,
times(x,cos(x)) != '+'(A,'+'(times(x,d(A)),d(B))),
inference(paramod,[status(thm)],[c_28,c_4990]) ).
cnf(c_4991,plain,
minus(cos(x)) = d(d(cos(x))),
inference(paramod,[status(thm)],[c_225,c_97]) ).
cnf(c_392,plain,
d(d(cos(x))) = minus(cos(x)),
inference(copy,[status(thm)],[c_4991]) ).
cnf(c_4992,plain,
times(x,cos(x)) != times(x,d(minus(d(A)))),
inference(paramod,[status(thm)],[c_186,c_253]) ).
cnf(c_4993,plain,
times(x,cos(x)) != times(x,minus(d(d(A)))),
inference(paramod,[status(thm)],[c_212,c_4992]) ).
cnf(c_4994,plain,
times(x,cos(x)) != minus(times(x,d(d(A)))),
inference(paramod,[status(thm)],[c_211,c_4993]) ).
cnf(c_1394,plain,
minus(times(x,d(d(A)))) != times(x,cos(x)),
inference(copy,[status(thm)],[c_4994]) ).
cnf(c_4995,plain,
minus(times(x,minus(cos(x)))) != times(x,cos(x)),
inference(paramod,[status(thm)],[c_392,c_1394]) ).
cnf(c_4996,plain,
minus(minus(times(x,cos(x)))) != times(x,cos(x)),
inference(paramod,[status(thm)],[c_211,c_4995]) ).
cnf(c_4997,plain,
times(x,cos(x)) != times(x,cos(x)),
inference(paramod,[status(thm)],[c_97,c_4996]) ).
cnf(c_4955,plain,
$false,
inference(copy,[status(thm)],[c_4997]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 22:13:49 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.31 % Process 1607250 was started by sandbox on n012,
% 0.04/0.31 % Sat Sep 26 22:13:49 2026
% 0.04/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.31
% 0.04/0.31 % From the command line: assign(max_seconds, 300).
% 30.89/4.25
% 30.89/4.25 % given #500 (T,wt=27): 726 d(cos(cos(one) + cos(cos(one) + cos(one)))) = zero. [para(676(a,1),143(a,1,1,1)),rewrite([1(10),8(12),33(2),1(10)]),flip(a)].
% 30.89/4.25
% 30.89/4.25 % given #1000 (F,wt=21): 4278 minus(times(x,d(cos(x)))) != times(x,cos(x)). [para(31(a,1),500(a,2)),rewrite([212(9),211(10)]),flip(a)].
% 30.89/4.25
% 30.89/4.25 % SZS status Unsatisfiable for theBenchmark
% 30.89/4.25
% 30.89/4.25 % Proof 1 at 2.67 (+ 1.10) seconds.
% 30.89/4.25 % Length of proof is 50.
% 30.89/4.25 % Level of proof is 11.
% 30.89/4.25 % Maximum clause weight is 29.000.
% 30.89/4.25 % Given clauses 1197.
% 30.89/4.25
% 30.89/4.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------