%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 : Fri Sep 25 12:55:49 PM UTC 2026
% Result : Unsatisfiable 27.53s 4.25s
% Output : CNFRefutation 27.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 76 ( 76 unt; 4 def)
% Number of atoms : 116 ( 75 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_plus) ).
fof(f2,axiom,
! [X2,X0,X1] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associtivity_of_plus) ).
fof(f3,axiom,
! [X0,X1] : times(X0,X1) = times(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_times) ).
fof(f4,axiom,
! [X2,X0,X1] : times(X0,times(X1,X2)) = times(times(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_times) ).
fof(f5,axiom,
! [X0] : '+'(zero,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
fof(f8,axiom,
! [X0] : times(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
fof(f10,axiom,
! [X0] : '+'(X0,minus(X0)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus) ).
fof(f11,plain,
! [X0] : zero = '+'(X0,minus(X0)),
inference(reorient_equations,[],[f10]) ).
fof(f14,axiom,
d(one) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_one) ).
fof(f15,plain,
zero = d(one),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
d(x) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_x) ).
fof(f17,plain,
one = d(x),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X0,X1] : d('+'(X0,X1)) = '+'(d(X0),d(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_plus) ).
fof(f19,axiom,
! [X0,X1] : d(times(X0,X1)) = '+'(times(X0,d(X1)),times(X1,d(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_times) ).
fof(f20,axiom,
! [X0] : d(sin(X0)) = times(cos(X0),d(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_sin) ).
fof(f21,axiom,
! [X0] : d(cos(X0)) = minus(times(sin(X0),d(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_cos) ).
fof(f22,negated_conjecture,
! [X0] : d(X0) != times(x,cos(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : times(X0,X1) = times(X1,X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : times(times(X0,X1),X2) = times(X0,times(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,plain,
! [X0: $i] : '+'(zero,X0) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_72,plain,
! [X0: $i] : times(one,X0) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_74,plain,
! [X0: $i] : '+'(X0,minus(X0)) = zero,
inference(cnf_transformation,[],[f11]) ).
tcf(c_76,plain,
d(one) = zero,
inference(cnf_transformation,[],[f15]) ).
tcf(c_77,plain,
d(x) = one,
inference(cnf_transformation,[],[f17]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : '+'(d(X0),d(X1)) = d('+'(X0,X1)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] : '+'(times(X0,d(X1)),times(X1,d(X0))) = d(times(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_80,plain,
! [X0: $i] : times(cos(X0),d(X0)) = d(sin(X0)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_81,plain,
! [X0: $i] : minus(times(sin(X0),d(X0))) = d(cos(X0)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_82,negated_conjecture,
! [X0: $i] : times(x,cos(x)) != d(X0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_138,definition,
iPr_def_10 = cos(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_139,definition,
iPr_def_11 = times(x,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_140,definition,
iPr_def_12 = d(x),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_141,definition,
iPr_def_13 = d(one),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_143,negated_conjecture,
! [X0: $i] : iPr_def_11 != d(X0),
inference(demodulation,[status(thm)],[c_82,c_138,c_139]) ).
tcf(c_144,plain,
! [X0: $i] : minus(times(sin(X0),d(X0))) = d(cos(X0)),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_145,plain,
! [X0: $i] : times(cos(X0),d(X0)) = d(sin(X0)),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] : '+'(times(X0,d(X1)),times(X1,d(X0))) = d(times(X0,X1)),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] : '+'(d(X0),d(X1)) = d('+'(X0,X1)),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_148,plain,
iPr_def_12 = one,
inference(demodulation,[status(thm)],[c_77,c_140]) ).
tcf(c_149,plain,
iPr_def_13 = zero,
inference(demodulation,[status(thm)],[c_76,c_141]) ).
tcf(c_151,plain,
! [X0: $i] : '+'(X0,minus(X0)) = zero,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_153,plain,
! [X0: $i] : times(one,X0) = X0,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_155,plain,
! [X0: $i] : '+'(zero,X0) = X0,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] : times(times(X0,X1),X2) = times(X0,times(X1,X2)),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] : times(X0,X1) = times(X1,X0),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] : '+'(X0,X1) = '+'(X1,X0),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_2920,plain,
d(iPr_def_12) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_141,c_148]) ).
tcf(c_2924,plain,
! [X0: $i] : times(iPr_def_12,X0) = X0,
inference(light_normalisation,[status(thm)],[c_153,c_148]) ).
tcf(c_2926,plain,
! [X0: $i] : '+'(iPr_def_13,X0) = X0,
inference(light_normalisation,[status(thm)],[c_155,c_149]) ).
tcf(c_2927,plain,
! [X0: $i] : '+'(X0,minus(X0)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_151,c_149]) ).
tcf(c_2931,plain,
times(iPr_def_10,x) = iPr_def_11,
inference(demodulation,[status(thm)],[c_139,c_157]) ).
tcf(c_2938,plain,
! [X0: $i] : times(X0,iPr_def_12) = X0,
inference(superposition,[status(thm)],[c_157,c_2924]) ).
tcf(c_2959,plain,
times(cos(x),iPr_def_12) = d(sin(x)),
inference(superposition,[status(thm)],[c_140,c_145]) ).
tcf(c_2968,plain,
times(iPr_def_12,cos(x)) = d(sin(x)),
inference(theory_normalisation,[status(thm)],[c_2959,c_158,c_159,c_156,c_157]) ).
tcf(c_2969,plain,
d(sin(x)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2968,c_138,c_2924]) ).
tcf(c_3032,plain,
minus(times(sin(x),iPr_def_12)) = d(cos(x)),
inference(superposition,[status(thm)],[c_140,c_144]) ).
tcf(c_3051,plain,
minus(times(iPr_def_12,sin(x))) = d(cos(x)),
inference(theory_normalisation,[status(thm)],[c_3032,c_158,c_159,c_156,c_157]) ).
tcf(c_3052,plain,
minus(sin(x)) = d(iPr_def_10),
inference(demodulation,[status(thm)],[c_3051,c_138,c_2924]) ).
tcf(c_3091,plain,
'+'(sin(x),d(iPr_def_10)) = iPr_def_13,
inference(superposition,[status(thm)],[c_3052,c_2927]) ).
tcf(c_3092,plain,
'+'(d(iPr_def_10),sin(x)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_3091,c_159]) ).
tcf(c_3715,plain,
! [X0: $i] : '+'(times(x,d(X0)),times(X0,iPr_def_12)) = d(times(x,X0)),
inference(superposition,[status(thm)],[c_140,c_146]) ).
tcf(c_3803,plain,
! [X0: $i] : '+'(times(X0,iPr_def_12),times(x,d(X0))) = d(times(x,X0)),
inference(theory_normalisation,[status(thm)],[c_3715,c_158,c_159,c_156,c_157]) ).
tcf(c_3804,plain,
! [X0: $i] : '+'(X0,times(x,d(X0))) = d(times(x,X0)),
inference(demodulation,[status(thm)],[c_3803,c_2938]) ).
tcf(c_4129,plain,
! [X0: $i] : '+'(d(X0),iPr_def_13) = d('+'(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_2920,c_147]) ).
tcf(c_4210,plain,
! [X0: $i,X1: $i] : '+'(d(X0),d(X1)) = d('+'(X1,X0)),
inference(superposition,[status(thm)],[c_147,c_159]) ).
tcf(c_4213,plain,
! [X0: $i] : '+'(iPr_def_13,d(X0)) = d('+'(X0,iPr_def_12)),
inference(theory_normalisation,[status(thm)],[c_4129,c_158,c_159,c_156,c_157]) ).
tcf(c_4214,plain,
! [X0: $i] : d('+'(X0,iPr_def_12)) = d(X0),
inference(demodulation,[status(thm)],[c_4213,c_2926]) ).
tcf(c_4562,plain,
! [X0: $i] : '+'(d(iPr_def_10),'+'(sin(x),X0)) = '+'(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_3092,c_158]) ).
tcf(c_4566,plain,
! [X0: $i] : '+'(d(iPr_def_10),'+'(sin(x),X0)) = X0,
inference(demodulation,[status(thm)],[c_4562,c_2926]) ).
tcf(c_4704,plain,
! [X0: $i] : d(X0) != iPr_def_11,
inference(superposition,[status(thm)],[c_4214,c_143]) ).
tcf(c_31621,plain,
'+'(d(iPr_def_10),d(times(x,sin(x)))) = times(x,d(sin(x))),
inference(superposition,[status(thm)],[c_3804,c_4566]) ).
tcf(c_31657,plain,
d('+'(iPr_def_10,times(x,sin(x)))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_31621,c_159,c_157,c_2931,c_2969,c_4210]) ).
tcf(c_31658,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_31657,c_4704]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 05:55:04 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 Running UEQ theorem proving
% 0.11/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.40
% 0.11/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.40
% 0.11/0.40 % Detected problem language: tptp
% 0.11/0.41 % Proving...
% 27.53/4.25 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 27.53/4.25 % SZS status Started for theBenchmark.p
% 27.53/4.25 % SZS status Unsatisfiable for theBenchmark.p
% 27.53/4.25
% 27.53/4.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.53/4.25
% 27.53/4.25 % ------ iProver source info
% 27.53/4.25
% 27.53/4.25 % git: date: 2026-07-19 20:42:38 +0200
% 27.53/4.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.53/4.25 % git: non_committed_changes: false
% 27.53/4.25
% 27.53/4.25 % ------ Parsing...% successful
% 27.53/4.25
% 27.53/4.25
% 27.53/4.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.53/4.25
% 27.53/4.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 27.53/4.25
% 27.53/4.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 27.53/4.25
% 27.53/4.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 27.53/4.25 % ------ Proving...
% 27.53/4.25 % ------ Problem Properties
% 27.53/4.25
% 27.53/4.25 %
% 27.53/4.25 % clauses 22
% 27.53/4.25 % conjectures 1
% 27.53/4.25 % EPR 3
% 27.53/4.25 % Horn 22
% 27.53/4.25 % unary 22
% 27.53/4.25 % binary 0
% 27.53/4.25 % lits 22
% 27.53/4.25 % lits eq 22
% 27.53/4.25 % fd_pure 0
% 27.53/4.25 % fd_pseudo 0
% 27.53/4.25 % fd_cond 0
% 27.53/4.25 % fd_pseudo_cond 0
% 27.53/4.25 % AC symbols 2
% 27.53/4.25
% 27.53/4.25 % ------ Input Options Time Limit: Unbounded
% 27.53/4.25
% 27.53/4.25
% 27.53/4.25 % ------
% 27.53/4.25 % Current options:
% 27.53/4.25 % ------
% 27.53/4.25
% 27.53/4.25
% 27.53/4.25 %
% 27.53/4.25
% 27.53/4.25 % ------ Proving...
% 27.53/4.25 %
% 27.53/4.25
% 27.53/4.25 % SZS status Unsatisfiable for theBenchmark.p
% 27.53/4.25
% 27.53/4.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.53/4.25
% 27.53/4.25
%------------------------------------------------------------------------------