%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV592-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:35:47 AM UTC 2025
% Result : Unsatisfiable 0.57s 0.78s
% Output : Proof 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 79 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 166 ( 108 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 147 ( 65 ~; 61 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 144 ( 133 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Transcendental_Osin_type,type,
c_Transcendental_Osin: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Transcendental_Opi_type,type,
c_Transcendental_Opi: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_Transcendental_Ocos_type,type,
c_Transcendental_Ocos: $i > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(1,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
tff(3,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
<=> ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
tff(8,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) = v_x ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) = v_x ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) = v_x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) = v_x ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) = v_x,
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
v_x = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
c_Transcendental_Osin(v_x) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(v_x),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
^ [V_x: $i] :
refl(( ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) )
<=> ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) )
<=> ! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) )
<=> ! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__periodic__pi_0) ).
tff(22,plain,
! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [V_x: $i] : ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) )
| ( c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
^ [V_x: $i,V_y: $i] :
refl(( ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__diff2_0) ).
tff(32,plain,
! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
tff(41,plain,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
<=> ( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
tff(46,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[51,48,41]) ).
tff(53,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
^ [V_x: $i,V_y: $i] :
refl(( ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__diff_0) ).
tff(58,plain,
! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Ocos(v_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( ~ ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[63,34]) ).
tff(65,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(v_x),
inference(transitivity,[status(thm)],[65,62,53,38,27,17]) ).
tff(67,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[70,48,41]) ).
tff(72,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [V_x: $i,V_y: $i] : ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(v_x),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[73,60]) ).
tff(75,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[74,72,67]) ).
tff(76,plain,
( ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) != c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
<=> ( c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) != c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) != c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(78,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) != c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV592-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 10:28:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.57/0.78 % SZS status Unsatisfiable
% 0.57/0.78 % SZS output start Proof
% See solution above
% 0.63/0.83 % E exiting
%------------------------------------------------------------------------------